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AlgebraQuestion and Answers: Page 289

Question Number 78449 Answers: 1 Comments: 1

find the domain of definition of f(x)=((−x)/(∣x∣−x))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{definition}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left({x}\right)=\frac{−{x}}{\mid{x}\mid−{x}} \\ $$

Question Number 78444 Answers: 0 Comments: 0

Question Number 78440 Answers: 0 Comments: 0

ab = p (a−2b)(a+b)(a+2b)=−24q Find ((a+b)/3) in terms of p, q.

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}\:=\:{p} \\ $$$$\:\:\left({a}−\mathrm{2}{b}\right)\left({a}+{b}\right)\left({a}+\mathrm{2}{b}\right)=−\mathrm{24}{q} \\ $$$${Find}\:\:\:\frac{{a}+{b}}{\mathrm{3}}\:\:\:\:{in}\:{terms}\:{of}\:{p},\:{q}. \\ $$

Question Number 78399 Answers: 2 Comments: 14

dear sir W, Mjs the set {1,4,n} have the condition that if two different elements are selected and 2112 is added to the result , then the result is a perfect square if n is a positif number . then the number of possible values of n is (A) 8 (B) 7 (C) 6 (D) 5 (E) 4

$${dear}\:{sir}\:{W},\:{Mjs}\: \\ $$$${the}\:{set}\:\left\{\mathrm{1},\mathrm{4},{n}\right\}\:{have}\:{the}\:{condition}\:{that}\: \\ $$$${if}\:{two}\:{different}\:{elements}\:{are} \\ $$$${selected}\:{and}\:\mathrm{2112}\:{is}\:{added}\:{to} \\ $$$${the}\:{result}\:,\:{then}\:{the}\:{result}\: \\ $$$${is}\:{a}\:{perfect}\:{square}\:{if}\:{n}\:{is}\:{a}\: \\ $$$${positif}\:{number}\:.\:{then}\:{the}\:{number}\: \\ $$$${of}\:{possible}\:{values}\:{of}\:{n}\:{is}\: \\ $$$$\left({A}\right)\:\mathrm{8}\:\:\:\:\left({B}\right)\:\mathrm{7}\:\:\:\:\:\left({C}\right)\:\mathrm{6}\:\:\:\:\:\left({D}\right)\:\mathrm{5} \\ $$$$\left({E}\right)\:\mathrm{4} \\ $$

Question Number 78390 Answers: 1 Comments: 0

solve for different digits a,b,c,d such that abcd=(ab+cd)^2 .

$${solve}\:{for}\:\boldsymbol{{different}}\:{digits}\:{a},{b},{c},{d}\: \\ $$$${such}\:{that}\:\boldsymbol{{abcd}}=\left(\boldsymbol{{ab}}+\boldsymbol{{cd}}\right)^{\mathrm{2}} . \\ $$

Question Number 78358 Answers: 0 Comments: 1

Q. solve (2^(sin^2 (x)) /(sin^2 (x) )) + (3^(cos^2 (x)) /(cos^2 (x))) = 6

$${Q}.\:{solve} \\ $$$$ \\ $$$$\frac{\mathrm{2}^{{sin}^{\mathrm{2}} \left({x}\right)} }{{sin}^{\mathrm{2}} \left({x}\right)\:}\:+\:\frac{\mathrm{3}^{{cos}^{\mathrm{2}} \left({x}\right)} }{{cos}^{\mathrm{2}} \left({x}\right)}\:=\:\mathrm{6} \\ $$

Question Number 78357 Answers: 2 Comments: 7

Show that: (((√(1 + 6x)) − (1/(√(1 − 6x))))/((√(1 + 3x)) − (1/(√(1 − 3x))))) = 4 + 6x Ignoring higher power of x in the expansion

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\frac{\sqrt{\mathrm{1}\:+\:\mathrm{6x}}\:\:−\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}\:−\:\mathrm{6x}}}}{\sqrt{\mathrm{1}\:+\:\mathrm{3x}}\:\:−\:\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}\:−\:\mathrm{3x}}}}\:\:\:\:\:=\:\:\:\mathrm{4}\:+\:\mathrm{6x} \\ $$$$\mathrm{Ignoring}\:\mathrm{higher}\:\mathrm{power}\:\mathrm{of}\:\:\mathrm{x}\:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$

Question Number 78351 Answers: 2 Comments: 1

Let a,b,c ∈ R^+ and (a+b)(b+c) = 1 , where 0 <b≤ 1 . Prove that ∣a−b∣∣b−c∣ ≥ ((∣(√a)−(√b)∣∣(√b)−(√c)∣)/2) .

$$\mathrm{Let}\:\:{a},{b},{c}\:\in\:\mathrm{R}^{+} \:\:\mathrm{and}\:\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{1}\:,\:\mathrm{where}\:\:\mathrm{0}\:<{b}\leqslant\:\mathrm{1}\:. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mid{a}−{b}\mid\mid{b}−{c}\mid\:\geqslant\:\frac{\mid\sqrt{{a}}−\sqrt{{b}}\mid\mid\sqrt{{b}}−\sqrt{{c}}\mid}{\mathrm{2}}\:. \\ $$

Question Number 78353 Answers: 0 Comments: 0

Question Number 78340 Answers: 2 Comments: 0

Let a,b,c > 0 and c^2 = ((ab+bc+ca)/3) . Prove that ((a^3 +b^3 −2c^3 )/(a^3 +b^3 +c^3 )) ≤ 3(((a^2 +b^2 −2c^2 )/(a^2 +b^2 +c^2 )))

$$\mathrm{Let}\:\:{a},{b},{c}\:>\:\mathrm{0}\:\:\mathrm{and}\:\:{c}^{\mathrm{2}} \:=\:\frac{{ab}+{bc}+{ca}}{\mathrm{3}}\:.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} −\mathrm{2}{c}^{\mathrm{3}} }{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }\:\leqslant\:\mathrm{3}\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{c}^{\mathrm{2}} }{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }\right) \\ $$

Question Number 78335 Answers: 1 Comments: 0

find the solution of (x/((x−2)^3 +(x−3)^3 −1)) ≥ 0

$${find}\:{the}\:{solution}\:{of} \\ $$$$\frac{{x}}{\left({x}−\mathrm{2}\right)^{\mathrm{3}} +\left({x}−\mathrm{3}\right)^{\mathrm{3}} −\mathrm{1}}\:\geqslant\:\mathrm{0} \\ $$

Question Number 78319 Answers: 0 Comments: 1

57+6h=16h−33

$$\mathrm{57}+\mathrm{6}{h}=\mathrm{16}{h}−\mathrm{33} \\ $$

Question Number 78306 Answers: 1 Comments: 0

The sum of age of Hamadou his wife and theirs son is 100. n years ago the wife had the quadruple of his son′s age and Hamadou was 6 time older than his son. Determine theirs ages. i want that you help me to found equations. i found the first : x+y+z=100 please help me for the rest.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{age}\:\mathrm{of}\:\mathrm{Hamadou}\:\:\: \\ $$$$\mathrm{his}\:\mathrm{wife}\:\mathrm{and}\:\mathrm{theirs}\:\mathrm{son}\:\mathrm{is}\:\mathrm{100}. \\ $$$$\mathrm{n}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the}\:\mathrm{wife}\:\mathrm{had}\:\mathrm{the}\: \\ $$$$\mathrm{quadruple}\:\mathrm{of}\:\mathrm{his}\:\mathrm{son}'\mathrm{s}\:\mathrm{age}\:\mathrm{and}\: \\ $$$$\mathrm{Hamadou}\:\mathrm{was}\:\mathrm{6}\:\mathrm{time}\:\mathrm{older}\:\mathrm{than} \\ $$$$\mathrm{his}\:\mathrm{son}. \\ $$$$\mathrm{Determine}\:\mathrm{theirs}\:\mathrm{ages}. \\ $$$$ \\ $$$$\mathrm{i}\:\mathrm{want}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{found} \\ $$$$\mathrm{equations}. \\ $$$$\mathrm{i}\:\mathrm{found}\:\mathrm{the}\:\mathrm{first}\::\:{x}+{y}+{z}=\mathrm{100} \\ $$$${please}\:{help}\:{me}\:{for}\:{the}\:{rest}. \\ $$

Question Number 78233 Answers: 0 Comments: 8

given 5x+22y=18 find for x,y integer

$${given}\:\mathrm{5}{x}+\mathrm{22}{y}=\mathrm{18} \\ $$$${find}\:{for}\:{x},{y}\:{integer} \\ $$

Question Number 78177 Answers: 1 Comments: 10

what equation of ellips with F_1 (1,2) F_2 (3,4) and a = (√3)

$${what}\:{equation}\:{of}\:{ellips} \\ $$$${with}\:{F}_{\mathrm{1}} \left(\mathrm{1},\mathrm{2}\right)\:{F}_{\mathrm{2}} \left(\mathrm{3},\mathrm{4}\right)\:{and}\:{a}\:=\:\sqrt{\mathrm{3}} \\ $$

Question Number 78168 Answers: 0 Comments: 6

Solve for x, y, z if: x^3 + y^3 + z^3 = 42

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z}\:\:\mathrm{if}:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:\:=\:\:\mathrm{42} \\ $$

Question Number 78162 Answers: 0 Comments: 4

Find the sum of nth term Σ_(k = 1) ^n (1/k^2 )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\:\:\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} } \\ $$

Question Number 78147 Answers: 0 Comments: 0

Question Number 78108 Answers: 1 Comments: 1

Question Number 78102 Answers: 1 Comments: 1

Question Number 78049 Answers: 2 Comments: 1

Question Number 78040 Answers: 1 Comments: 4

Question Number 78037 Answers: 0 Comments: 11

Question Number 77991 Answers: 2 Comments: 0

If P_1 P_2 P_3 will be taken as point in an Argand diagram representing complex number Z_1 ,Z_2 ,Z_3 and point P_(1 ) ,P_2 ,P_3 is an equalateral triangle.show that (Z_2 −Z_3 )^2 +(Z_3 −Z_1 )^2 +(Z_1 −Z_2 )^2 =0

$${If}\:\:{P}_{\mathrm{1}} \:\:{P}_{\mathrm{2}} \:\:{P}_{\mathrm{3}} \:\:{will}\:{be}\:{taken} \\ $$$${as}\:{point}\:{in}\:{an}\:{Argand} \\ $$$${diagram}\:{representing} \\ $$$${complex}\:{number} \\ $$$${Z}_{\mathrm{1}} ,{Z}_{\mathrm{2}} ,{Z}_{\mathrm{3}} \:\:{and}\:{point} \\ $$$${P}_{\mathrm{1}\:} ,{P}_{\mathrm{2}} ,{P}_{\mathrm{3}} \:{is}\:{an}\:{equalateral} \\ $$$${triangle}.{show}\:{that} \\ $$$$\left({Z}_{\mathrm{2}} −{Z}_{\mathrm{3}} \right)^{\mathrm{2}} +\left({Z}_{\mathrm{3}} −{Z}_{\mathrm{1}} \right)^{\mathrm{2}} +\left({Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 77990 Answers: 2 Comments: 0

Find the equation to the two circles each of which touch the three circle x^2 +y^2 =4a^2 x^2 +y^2 +2ax=0 x^2 +y^2 −2ax=0

$${Find}\:{the}\:{equation}\:{to}\:{the} \\ $$$${two}\:{circles}\:{each}\:{of} \\ $$$${which}\:{touch}\:{the}\:{three}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}{a}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{ax}=\mathrm{0} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{ax}=\mathrm{0} \\ $$$$ \\ $$

Question Number 77965 Answers: 1 Comments: 9

solve for x,y,z ∈N 35x+21y+60z=665

$${solve}\:{for}\:{x},{y},{z}\:\in\mathbb{N} \\ $$$$\mathrm{35}{x}+\mathrm{21}{y}+\mathrm{60}{z}=\mathrm{665} \\ $$

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