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AlgebraQuestion and Answers: Page 265

Question Number 80881 Answers: 1 Comments: 0

v=−(((2b+3cp)p)/(3+bp^2 )) ((3v^2 +2bpv+3cp+b)/(1+bp^2 +cp^3 )) > 0 b,c ∈ R , b<0 Any non-zero real value of p in terms of b,c obeying above condition?

$${v}=−\frac{\left(\mathrm{2}{b}+\mathrm{3}{cp}\right){p}}{\mathrm{3}+{bp}^{\mathrm{2}} } \\ $$$$\:\frac{\mathrm{3}{v}^{\mathrm{2}} +\mathrm{2}{bpv}+\mathrm{3}{cp}+{b}}{\mathrm{1}+{bp}^{\mathrm{2}} +{cp}^{\mathrm{3}} }\:>\:\mathrm{0}\:\: \\ $$$${b},{c}\:\in\:\mathbb{R}\:,\:{b}<\mathrm{0} \\ $$$${Any}\:{non}-{zero}\:{real}\:{value}\:{of}\:{p} \\ $$$${in}\:{terms}\:{of}\:{b},{c}\:\:{obeying}\:{above} \\ $$$${condition}? \\ $$

Question Number 80804 Answers: 2 Comments: 2

Find [(√1)]+[(√2)]+[(√3)]+...+[(√(100))]=? with [x]=greatest integer function can we find a general formula for [(√1)]+[(√2)]+[(√3)]+...+[(√n)] in terms of n?

$${Find} \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+...+\left[\sqrt{\mathrm{100}}\right]=? \\ $$$${with}\:\left[{x}\right]={greatest}\:{integer}\:{function} \\ $$$$ \\ $$$${can}\:{we}\:{find}\:{a}\:{general}\:{formula}\:{for}\: \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+...+\left[\sqrt{{n}}\right] \\ $$$${in}\:{terms}\:{of}\:{n}? \\ $$

Question Number 80760 Answers: 0 Comments: 1

Question Number 80832 Answers: 1 Comments: 2

Identifier les chiffres de l′addition decimale que voici : UN+DOUX+DOUX+DOUX +DOUX=NEUF

$$\boldsymbol{{Identifier}}\:\boldsymbol{{les}}\:\boldsymbol{{chiffres}}\:\boldsymbol{{de}} \\ $$$$\boldsymbol{{l}}'\boldsymbol{{addition}}\:\boldsymbol{{decimale}}\:\boldsymbol{{que}} \\ $$$$\boldsymbol{{voici}}\:: \\ $$$$\boldsymbol{\mathrm{UN}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}} \\ $$$$+\boldsymbol{\mathrm{DOUX}}=\boldsymbol{\mathrm{NEUF}} \\ $$

Question Number 80747 Answers: 1 Comments: 1

Question Number 80733 Answers: 0 Comments: 3

x^2 =2^x ⇒x=?

$$\mathrm{x}^{\mathrm{2}} =\mathrm{2}^{\mathrm{x}} \Rightarrow\mathrm{x}=? \\ $$

Question Number 80706 Answers: 1 Comments: 0

Question Number 80702 Answers: 1 Comments: 4

{ (((1/x)+(1/y)=34)),(((1/(√x))+(1/(√y))=23−(1/(√(xy))) )) :} find the solution.

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\mathrm{34}}\\{\frac{\mathrm{1}}{\sqrt{{x}}}+\frac{\mathrm{1}}{\sqrt{{y}}}=\mathrm{23}−\frac{\mathrm{1}}{\sqrt{{xy}}}\:}\end{cases} \\ $$$${find}\:{the}\:{solution}. \\ $$

Question Number 80645 Answers: 0 Comments: 11

if a_1 =2 a_(n+1) =a_n ^2 −1 find a_n =?

$${if} \\ $$$${a}_{\mathrm{1}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} ={a}_{{n}} ^{\mathrm{2}} −\mathrm{1} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 80643 Answers: 2 Comments: 0

Prove that there is no solution for 7^n ≡1 mod(35) with n∈N.

$${Prove}\:{that}\:{there}\:{is}\:{no}\:{solution}\:{for} \\ $$$$\mathrm{7}^{{n}} \equiv\mathrm{1}\:{mod}\left(\mathrm{35}\right)\:{with}\:{n}\in\mathbb{N}. \\ $$

Question Number 80607 Answers: 0 Comments: 0

Question Number 80580 Answers: 2 Comments: 0

Find general solution for k such that 7^k ≡1 mod (35)

$${Find}\:{general}\:{solution}\:{for}\:{k}\:{such}\:{that} \\ $$$$\mathrm{7}^{{k}} \equiv\mathrm{1}\:{mod}\:\left(\mathrm{35}\right) \\ $$

Question Number 80543 Answers: 1 Comments: 6

Question Number 80493 Answers: 0 Comments: 4

Solve for a, b and c a + b + c = (1/2) ..... (i) abc = − (1/4) ...... (iii) ab + ac + bc = (3/2) ...... (iv)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c} \\ $$$$\:\:\:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\mathrm{abc}\:\:\:=\:\:\:−\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:......\:\left(\mathrm{iii}\right) \\ $$$$\:\:\:\:\:\:\mathrm{ab}\:+\:\mathrm{ac}\:+\:\mathrm{bc}\:\:\:=\:\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\:\:......\:\left(\mathrm{iv}\right) \\ $$

Question Number 80503 Answers: 1 Comments: 0

prove that they are infinitely many primes

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{infinitely}\:\mathrm{many} \\ $$$$\mathrm{primes} \\ $$

Question Number 80448 Answers: 1 Comments: 3

Hello All of You verry Nice Day, God bless You love peace and happiness Solve for (x,y)∈R^2 { ((x^2 +y^2 =2x+3y+1)),((x^4 +y^4 =4x^2 +9y^2 +12xy+2x^2 y^2 +18)) :}

$${Hello}\:{All}\:{of}\:{You}\:{verry}\:{Nice}\:{Day},\:{God}\:{bless}\:{You}\:{love}\:{peace}\:{and}\: \\ $$$${happiness}\: \\ $$$${Solve}\:{for}\:\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \: \\ $$$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{x}+\mathrm{3}{y}+\mathrm{1}}\\{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} =\mathrm{4}{x}^{\mathrm{2}} +\mathrm{9}{y}^{\mathrm{2}} +\mathrm{12}{xy}+\mathrm{2}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{18}}\end{cases} \\ $$$$ \\ $$

Question Number 80433 Answers: 1 Comments: 6

find the solution of (√(4−x))−2≤x∣x−3∣+4x

$${find}\:{the}\:{solution}\:{of} \\ $$$$\sqrt{\mathrm{4}−{x}}−\mathrm{2}\leqslant{x}\mid{x}−\mathrm{3}\mid+\mathrm{4}{x} \\ $$

Question Number 80405 Answers: 1 Comments: 11

Solve: (a) (x − 3)^2 > − 5 (b) 3x^2 > − 12

$$\mathrm{Solve}: \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\:\:\:\:\:\left(\mathrm{x}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:\:>\:\:−\:\mathrm{5} \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3x}^{\mathrm{2}} \:\:>\:\:−\:\mathrm{12} \\ $$

Question Number 80404 Answers: 1 Comments: 0