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AlgebraQuestion and Answers: Page 71

Question Number 192957 Answers: 4 Comments: 2

bx^3 =10a^2 bx + 3a^3 y , ay^3 = 10ab^2 y + 3b^3 x solve for x and y in terms of (a , b) and solve for a and b in terms of (x , y )

$$ \\ $$$${bx}^{\mathrm{3}} =\mathrm{10}{a}^{\mathrm{2}} {bx}\:+\:\mathrm{3}{a}^{\mathrm{3}} {y}\:,\:{ay}^{\mathrm{3}} =\:\mathrm{10}{ab}^{\mathrm{2}} {y}\:+\:\mathrm{3}{b}^{\mathrm{3}} {x} \\ $$$${solve}\:{for}\:{x}\:{and}\:{y}\:{in}\:{terms}\:{of}\:\left({a}\:,\:{b}\right) \\ $$$${and}\:{solve}\:{for}\:{a}\:{and}\:{b}\:{in}\:{terms}\:{of}\:\:\left({x}\:,\:{y}\:\right) \\ $$

Question Number 192942 Answers: 2 Comments: 1

Question Number 192937 Answers: 0 Comments: 0

Question Number 192936 Answers: 2 Comments: 0

Question Number 192928 Answers: 1 Comments: 0

2x^2 −6x+k = 0 where k<0 ((α/β) + (β/α))_(max) = ?

$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}+{k}\:=\:\mathrm{0}\:{where}\:{k}<\mathrm{0}\: \\ $$$$\left(\frac{\alpha}{\beta}\:+\:\frac{\beta}{\alpha}\right)_{\mathrm{max}} \:=\:? \\ $$

Question Number 192925 Answers: 1 Comments: 0

Find: x = ? 1. 2^(x+1) + 0,5^(x−2) = 9 2. 4^(3x) = 12 3. 6^(x+2) = 18

$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\mathrm{2}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:+\:\mathrm{0},\mathrm{5}^{\boldsymbol{\mathrm{x}}−\mathrm{2}} \:=\:\mathrm{9} \\ $$$$\mathrm{2}.\:\mathrm{4}^{\mathrm{3}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{12} \\ $$$$\mathrm{3}.\:\mathrm{6}^{\boldsymbol{\mathrm{x}}+\mathrm{2}} \:=\:\mathrm{18} \\ $$

Question Number 192924 Answers: 2 Comments: 0

1•determiner: tan (x/2) en fonction de tan x 2•on donne tan x=(1/8) tan (x/2)=? 3• la valeur proche de x?

$$\mathrm{1}\bullet\mathrm{determiner}:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{tan}\:\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{2}\bullet\mathrm{on}\:\mathrm{donne}\:\:\mathrm{tan}\:\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{8}}\:\:\:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}=? \\ $$$$\mathrm{3}\bullet\:\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{proche}\:\mathrm{de}\:\boldsymbol{\mathrm{x}}? \\ $$

Question Number 192917 Answers: 1 Comments: 0

Question Number 192914 Answers: 1 Comments: 0

x^2 (x^2 −1)=(1−(c/x))^3 +((c/x))^3

$${x}^{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)=\left(\mathrm{1}−\frac{{c}}{{x}}\right)^{\mathrm{3}} +\left(\frac{{c}}{{x}}\right)^{\mathrm{3}} \\ $$

Question Number 192898 Answers: 0 Comments: 1

Solve for x x^3 −7x−2=0

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{7}{x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 192883 Answers: 1 Comments: 0

Question Number 192875 Answers: 2 Comments: 0

x^2 −yz=a^n y^2 −zx=b^n z^2 −xy=c^n find (x , y , z) in terms of (a , b , c)

$${x}^{\mathrm{2}} −{yz}={a}^{{n}} \\ $$$${y}^{\mathrm{2}} −{zx}={b}^{{n}} \\ $$$${z}^{\mathrm{2}} −{xy}={c}^{{n}} \\ $$$${find}\:\left({x}\:,\:{y}\:,\:{z}\right)\:{in}\:{terms}\:{of}\:\left({a}\:,\:{b}\:,\:{c}\right) \\ $$

Question Number 192862 Answers: 1 Comments: 0

Solve for x x^3 −115x+150=0

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{115}{x}+\mathrm{150}=\mathrm{0} \\ $$

Question Number 192856 Answers: 2 Comments: 0

if a+b+c +d = 63 and a,b,c,d ∈ N find the maximum value of ab+bc+cd = ?

$$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$

Question Number 192855 Answers: 2 Comments: 0

Question Number 192852 Answers: 2 Comments: 2

find the domain of thefunction f(x) = (1/( (√(x^2 −{x}^2 )))) where {.} is the fractional part function.

$$ \\ $$$${find}\:{the}\:{domain}\:{of}\:{thefunction} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left\{{x}\right\}^{\mathrm{2}} }}\:\:\:\:\:{where}\:\left\{.\right\}\:{is}\:{the}\:{fractional}\:{part}\:{function}. \\ $$

Question Number 192851 Answers: 0 Comments: 1

Solve: ((log_(a^2 (√x)) a)/(log_(2x) a)) + log_(ax) a . log_(1/a) 2x = 0

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{log}_{{a}^{\mathrm{2}} \sqrt{{x}}} \:{a}}{\mathrm{log}_{\mathrm{2}{x}} \:{a}}\:+\:\mathrm{log}_{{ax}} \:{a}\:.\:\mathrm{log}_{\frac{\mathrm{1}}{{a}}} \:\mathrm{2}{x}\:=\:\mathrm{0} \\ $$

Question Number 192839 Answers: 2 Comments: 0

Question Number 192811 Answers: 1 Comments: 0

Question Number 192793 Answers: 2 Comments: 0

x^4 +x^3 +x^2 +x+1=y^2 where y is positive integer number then find the positive integal values of (x) for which that holds

$$\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{1}=\boldsymbol{{y}}^{\mathrm{2}} \:\boldsymbol{{where}}\:\boldsymbol{{y}}\:\boldsymbol{{is}}\:\boldsymbol{{positive}}\:\boldsymbol{{integer}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{positive}}\:\boldsymbol{{integal}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{which}}\:\boldsymbol{{that}}\:\boldsymbol{{holds}} \\ $$

Question Number 192786 Answers: 1 Comments: 0

N=<aabb>∈N & N is perfect square find N ?

$${N}=<{aabb}>\in\mathbb{N}\:\:\&\:\:{N}\:\:{is}\:\:{perfect}\:{square} \\ $$$${find}\:\:{N}\:\:? \\ $$$$ \\ $$

Question Number 192780 Answers: 1 Comments: 1

Question Number 192777 Answers: 0 Comments: 2

(√(x^2 +ax−1))−(√(x^2 +bx−1))=(√a)−(√b) find x .

$$\sqrt{{x}^{\mathrm{2}} +{ax}−\mathrm{1}}−\sqrt{{x}^{\mathrm{2}} +{bx}−\mathrm{1}}=\sqrt{{a}}−\sqrt{{b}} \\ $$$${find}\:{x}\:. \\ $$

Question Number 192721 Answers: 1 Comments: 0

x^3 −3xy^2 =18 3x^2 y−y^3 =26 and what do you recommend to read to deal with such problems

$$ \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{18} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{26} \\ $$$${and}\:{what}\:{do}\:{you}\:{recommend}\:{to}\:{read}\:{to}\:{deal} \\ $$$${with}\:{such}\:{problems} \\ $$

Question Number 192720 Answers: 4 Comments: 0

Question Number 192697 Answers: 1 Comments: 0

Find the value of (9x−(1/(100))x)^3 (9x−(2/(100))x)^3 (9x−(3/(100))x)^3 ...(9x−((2013)/(100))x)^3 .

$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} ...\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$

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