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AlgebraQuestion and Answers: Page 57

Question Number 200739 Answers: 3 Comments: 2

solve for x∈R x^3 −3((3x−2))^(1/3) +2=0

$${solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−\mathrm{2}}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 200729 Answers: 1 Comments: 0

if a<b<0 and (√( a^4 +2a^2 b^2 +b^4 )) +(√(a^4 −2a^2 b^2 +b^4 )) = ?

$$ \\ $$$$\:\:\:{if}\:\:\:\:{a}<{b}<\mathrm{0}\:\:\: \\ $$$$\:\:\:{and}\:\:\sqrt{\:{a}^{\mathrm{4}} +\mathrm{2}{a}^{\mathrm{2}} {b}^{\mathrm{2}} +{b}^{\mathrm{4}} }\:+\sqrt{{a}^{\mathrm{4}} −\mathrm{2}{a}^{\mathrm{2}} {b}^{\mathrm{2}} +{b}^{\mathrm{4}} }\:=\:? \\ $$$$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 200723 Answers: 0 Comments: 0

Question Number 200718 Answers: 3 Comments: 0

3. 1+3+5+7+...+(2n+1) = ?

$$\mathrm{3}. \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+...+\left(\mathrm{2}{n}+\mathrm{1}\right)\:=\:? \\ $$

Question Number 200717 Answers: 1 Comments: 0

2. A = 12 − 2x B = 3 + 2x (A∙B)_(min) = ?

$$\mathrm{2}. \\ $$$${A}\:=\:\mathrm{12}\:−\:\mathrm{2}{x} \\ $$$${B}\:=\:\mathrm{3}\:+\:\mathrm{2}{x} \\ $$$$\left({A}\centerdot{B}\right)_{\boldsymbol{{min}}} \:=\:? \\ $$

Question Number 200716 Answers: 1 Comments: 0

1. (a/8) + (b/5) = 6 ⇒ (a+b)_(max) = ?

$$\mathrm{1}.\: \\ $$$$\frac{{a}}{\mathrm{8}}\:+\:\frac{{b}}{\mathrm{5}}\:=\:\mathrm{6}\:\:\:\Rightarrow\:\:\:\left({a}+{b}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$

Question Number 200696 Answers: 4 Comments: 0

Question Number 200589 Answers: 1 Comments: 0

Question Number 200565 Answers: 1 Comments: 2

sin^(10) x + cos^(10) x = ((29)/(16)) cos^4 2x find: x = ?

$$\mathrm{sin}^{\mathrm{10}} \mathrm{x}\:\:+\:\:\mathrm{cos}^{\mathrm{10}} \mathrm{x}\:\:=\:\:\frac{\mathrm{29}}{\mathrm{16}}\:\mathrm{cos}^{\mathrm{4}} \mathrm{2x} \\ $$$$\mathrm{find}:\:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 200594 Answers: 2 Comments: 0

Question Number 200498 Answers: 5 Comments: 3

solve for x∈R (√(x−(1/x)))+(√(1−(1/x)))=x

$${solve}\:{for}\:{x}\in{R} \\ $$$$\sqrt{{x}−\frac{\mathrm{1}}{{x}}}+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}={x} \\ $$

Question Number 200472 Answers: 0 Comments: 0

Question Number 200465 Answers: 2 Comments: 1

Find the sum of the fifth powers of the roots of x^3 −2x^2 +x−1=0 by applying synthetic division

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fifth}\:\mathrm{powers}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}=\mathrm{0}\:\mathrm{by} \\ $$$$\mathrm{applying}\:\mathrm{synthetic}\:\mathrm{division} \\ $$

Question Number 200460 Answers: 1 Comments: 0

Find the cardano′s solution of the equation 28x^3 −9x^2 +1=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cardano}'\mathrm{s}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{equation}\:\mathrm{28x}^{\mathrm{3}} −\mathrm{9x}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$

Question Number 200459 Answers: 0 Comments: 1

In the equation x^3 −x−1=0, find the value of s_6 .

$$\mathrm{In}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}−\mathrm{1}=\mathrm{0},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{s}_{\mathrm{6}} . \\ $$

Question Number 200450 Answers: 1 Comments: 0

if ((sin4x)/(cos6x)) = 0 find x = ?

$${if}\:\:\:\frac{{sin}\mathrm{4}{x}}{{cos}\mathrm{6}{x}}\:=\:\mathrm{0}\:\:\:{find}\:\:\:{x}\:=\:? \\ $$

Question Number 200446 Answers: 1 Comments: 0

fund Σ_(n=1) ^∞ (((3 + (−1)^n )^n )/n) x^n = ?

$${fund}\:\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(\mathrm{3}\:+\:\left(−\mathrm{1}\right)^{\boldsymbol{{n}}} \right)^{\boldsymbol{{n}}} }{{n}}\:{x}^{\boldsymbol{{n}}} \:=\:? \\ $$

Question Number 200438 Answers: 0 Comments: 1

Find: (√(3 + (√(6 + (√(9 + ... + (√(96 + (√(99)))))))))) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{3}\:+\:\sqrt{\mathrm{6}\:+\:\sqrt{\mathrm{9}\:+\:...\:+\:\sqrt{\mathrm{96}\:+\:\sqrt{\mathrm{99}}}}}}\:=\:? \\ $$

Question Number 200432 Answers: 0 Comments: 2

Question Number 200424 Answers: 0 Comments: 4

Question Number 200417 Answers: 1 Comments: 0

find: Ω = ∫_1 ^( ∞) ((√x)/((1 + x^2 ))) dx = ?

$$\mathrm{find}:\:\:\:\Omega\:=\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{\sqrt{\mathrm{x}}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 200415 Answers: 1 Comments: 0

Question Number 200412 Answers: 1 Comments: 0

If (√((x-6)^2 + (y+1)^2 )) + (√((x-9)^2 + (y+5)^2 )) find: minumum = ?

$$\mathrm{If} \\ $$$$\sqrt{\left(\mathrm{x}-\mathrm{6}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} }\:+\:\sqrt{\left(\mathrm{x}-\mathrm{9}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}+\mathrm{5}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\mathrm{find}:\:\:\:\mathrm{minumum}\:=\:? \\ $$

Question Number 200388 Answers: 1 Comments: 0

find all values for k such that the eq. x^3 −13x+k=0 has three integer roots.

$${find}\:{all}\:{values}\:{for}\:{k}\:{such}\:{that}\:{the}\:{eq}. \\ $$$${x}^{\mathrm{3}} −\mathrm{13}{x}+{k}=\mathrm{0}\:{has}\:{three}\:{integer}\:{roots}. \\ $$

Question Number 200353 Answers: 3 Comments: 0

If the roots of x^3 +3px^2 +3qx+r=0 are in harmonic progression, then prove that 2q^3 =r(3pq−r)

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{3px}^{\mathrm{2}} +\mathrm{3qx}+\mathrm{r}=\mathrm{0}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{harmonic}\:\mathrm{progression},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{2q}^{\mathrm{3}} =\mathrm{r}\left(\mathrm{3pq}−\mathrm{r}\right) \\ $$

Question Number 200351 Answers: 1 Comments: 0

Solve the equation x^3 −12x^2 −6x−10=0 by cardon′s method

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{12x}^{\mathrm{2}} −\mathrm{6x}−\mathrm{10}=\mathrm{0}\: \\ $$$$\mathrm{by}\:\mathrm{cardon}'\mathrm{s}\:\mathrm{method} \\ $$

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