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AlgebraQuestion and Answers: Page 85

Question Number 187971 Answers: 2 Comments: 0

If , x^( 5) = 1 ∧ x≠1 ( (( 1)/(x^( 2) −x +1)) + (1/(x^( 2) + x +1)) )^( 10) = ?

$$ \\ $$$$\:\:\mathrm{If}\:\:\:,\:\:{x}^{\:\mathrm{5}} \:=\:\mathrm{1}\:\:\:\wedge\:\:{x}\neq\mathrm{1} \\ $$$$ \\ $$$$\:\:\:\:\left(\:\frac{\:\mathrm{1}}{{x}^{\:\mathrm{2}} \:−{x}\:+\mathrm{1}}\:+\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} \:+\:{x}\:+\mathrm{1}}\:\right)^{\:\mathrm{10}} =\:? \\ $$$$ \\ $$

Question Number 187916 Answers: 1 Comments: 0

how is solution y=(cosx)^((3x^2 −1)^e^x ) (dy/dx)=?

$${how}\:{is}\:{solution} \\ $$$${y}=\left({cosx}\right)^{\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)^{{e}^{{x}} } } \\ $$$$\frac{{dy}}{{dx}}=? \\ $$

Question Number 187908 Answers: 0 Comments: 0

Question Number 187905 Answers: 0 Comments: 1

Question Number 187877 Answers: 2 Comments: 0

Simplify completely ((256^(−(7/(16))) × 128^(9/(28)) )/(512^((17)/(36)) × 64^(−((11)/(12))) ))

$$\mathrm{Simplify}\:\mathrm{completely} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{256}^{−\frac{\mathrm{7}}{\mathrm{16}}} \:×\:\mathrm{128}^{\frac{\mathrm{9}}{\mathrm{28}}} }{\mathrm{512}^{\frac{\mathrm{17}}{\mathrm{36}}} \:×\:\mathrm{64}^{−\frac{\mathrm{11}}{\mathrm{12}}} } \\ $$

Question Number 187874 Answers: 2 Comments: 0

how is solution ((√2)−1)^(13) =x ((√2)+1)^(221) =? 1)x^(−16) 2)x^(−17) 3)x^(221) 4)x^(21)

$${how}\:{is}\:{solution} \\ $$$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{13}} =\mathrm{x}\:\:\:\:\:\:\:\:\:\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{221}} =? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{x}^{−\mathrm{16}} \left.\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{x}^{−\mathrm{17}} \:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{x}^{\mathrm{221}} \:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{x}^{\mathrm{21}} \\ $$

Question Number 187871 Answers: 1 Comments: 0

how is solution sgn(cos((21)/(10)))=?

$${how}\:{is}\:{solution} \\ $$$$\mathrm{sgn}\left(\mathrm{cos}\frac{\mathrm{21}}{\mathrm{10}}\right)=? \\ $$

Question Number 187856 Answers: 1 Comments: 0

find x 2^(√x) =8x

$${find}\:{x} \\ $$$$\mathrm{2}^{\sqrt{{x}}} =\mathrm{8}{x} \\ $$

Question Number 187951 Answers: 3 Comments: 0

please help me to solve 6x^2 +x−2=0

$${please}\:{help}\:{me}\:{to}\:{solve} \\ $$$$\mathrm{6}{x}^{\mathrm{2}} +{x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 187811 Answers: 1 Comments: 0

Question Number 187780 Answers: 1 Comments: 0

solve ⌊ (1/(4 )) + 2^( x) ⌋ + ⌊ (1/2) + 2^( x+1) ⌋=1

$$ \\ $$$$\:\:{solve} \\ $$$$\:\:\:\:\lfloor\:\:\frac{\mathrm{1}}{\mathrm{4}\:}\:+\:\mathrm{2}^{\:{x}} \:\rfloor\:+\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}^{\:{x}+\mathrm{1}} \:\rfloor=\mathrm{1} \\ $$$$ \\ $$

Question Number 187731 Answers: 4 Comments: 0

Question Number 187695 Answers: 2 Comments: 0

If , f( x )= (( sin_ (cos (x) ))/( ^ (√( (π/x))))) ⇒ f ′ ((( π)/2) ) = ?

$$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$

Question Number 187690 Answers: 0 Comments: 0

Question Number 187595 Answers: 1 Comments: 1

Question Number 187556 Answers: 0 Comments: 1

Question Number 187534 Answers: 0 Comments: 0

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Question Number 187496 Answers: 1 Comments: 1

Question Number 187478 Answers: 1 Comments: 0

let a and b be positive integers such that ab + 1 divides a^2 + b^2 . show that ((a^2 + b^2 )/(ab + 1)) is the sequare of an integer.

$$\: \\ $$$$\:\:\:\boldsymbol{{let}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{ab}}\:+\:\mathrm{1}\:\boldsymbol{{divides}}\:\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} .\:\:\:\:\: \\ $$$$\:\:\:\:\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{ab}}\:+\:\mathrm{1}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{sequare}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\:\boldsymbol{{integer}}. \\ $$$$ \\ $$

Question Number 187476 Answers: 1 Comments: 0

Question Number 187442 Answers: 1 Comments: 0

If (7^x /(1 + 7^x )) = (3/7) find ((2401^x )/(1 + 2401^x )) = ?

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{7}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:? \\ $$

Question Number 187440 Answers: 0 Comments: 1

if y^(x−y) =(x^2 /y) then x−y=?

$${if}\:\:{y}^{{x}−{y}} =\frac{{x}^{\mathrm{2}} }{{y}}\:{then}\:{x}−{y}=? \\ $$

Question Number 187437 Answers: 1 Comments: 0

Question Number 187388 Answers: 2 Comments: 0

p^3 +q^3 =c , pq=(1/3) ∀ 0<c<(2/(3(√3))) Find p+q.

$${p}^{\mathrm{3}} +{q}^{\mathrm{3}} ={c}\:\:\:,\:\:{pq}=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\forall\:\:\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${Find}\:{p}+{q}. \\ $$

Question Number 187381 Answers: 2 Comments: 0

3^x =5^y =225 Determiner: (1/x)+(1/y) ?

$$\mathrm{3}^{{x}} =\mathrm{5}^{{y}} =\mathrm{225} \\ $$$${Determiner}:\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:? \\ $$

Question Number 187373 Answers: 0 Comments: 0

Solve for natural numbers: 31 + Σ_(k=1) ^n ( ((n),(k) ) ∙ Σ_(m=1) ^n m^(n−k) ) = 31^(30)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$

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