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AlgebraQuestion and Answers: Page 269

Question Number 82877 Answers: 1 Comments: 1

1)find xy∈R 2)find x,y∈Z (x+2yi)^6 =8i

$$\left.\mathrm{1}\right){find}\:{xy}\in{R} \\ $$$$\left.\mathrm{2}\right){find}\:{x},{y}\in{Z} \\ $$$$\left({x}+\mathrm{2}{yi}\right)^{\mathrm{6}} =\mathrm{8}{i} \\ $$

Question Number 82701 Answers: 1 Comments: 0

2f(x−1) +3f(x+1) ^ = 3x^2 −5x find f(x)

$$\mathrm{2}{f}\left({x}−\mathrm{1}\right)\:+\mathrm{3}{f}\left({x}+\mathrm{1}\right)\overset{\:} {\:}=\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x} \\ $$$${find}\:{f}\left({x}\right) \\ $$

Question Number 82667 Answers: 1 Comments: 0

if a>0 b>0 a≤b show that a^2 ≤(((2ab)/(a+b)))^2 ≤ab≤(((a+b)/2))^2 ≤((a^2 +b^2 )/2)≤b^2

$${if}\:{a}>\mathrm{0}\:\:{b}>\mathrm{0}\:\:{a}\leqslant{b} \\ $$$$ \\ $$$${show}\:{that}\: \\ $$$${a}^{\mathrm{2}} \leqslant\left(\frac{\mathrm{2}{ab}}{{a}+{b}}\right)^{\mathrm{2}} \leqslant{ab}\leqslant\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} \leqslant\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}\leqslant{b}^{\mathrm{2}} \\ $$

Question Number 82665 Answers: 1 Comments: 2

(√(6561(√(6561(√(6561(√(6561(√(...)))))))))) = 3^( 8^x ) (√(6561(√(...)))) (60 time) find x

$$\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{...}}}}}\:=\:\mathrm{3}^{\:\mathrm{8}^{{x}} \:} \\ $$$$\sqrt{\mathrm{6561}\sqrt{...}}\:\:\left(\mathrm{60}\:{time}\right) \\ $$$${find}\:{x} \\ $$

Question Number 82644 Answers: 1 Comments: 2

Question Number 82596 Answers: 0 Comments: 4

Question Number 82593 Answers: 0 Comments: 3

Question Number 82589 Answers: 0 Comments: 1

Question Number 82582 Answers: 0 Comments: 2

solve x^3 −3x+1=0

$${solve} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 82570 Answers: 0 Comments: 1

if f(x) = f(x+1) − x find f(x)

$${if}\:{f}\left({x}\right)\:=\:{f}\left({x}+\mathrm{1}\right)\:−\:{x}\: \\ $$$${find}\:{f}\left({x}\right)\: \\ $$

Question Number 82561 Answers: 1 Comments: 0

a polynomial gives a remainder of −x−1 when divided by x^(2.) and a remainder of −1 when divided by x−1 . what is the remainder when the polynomial divided by x^2 (x−1) ?

$${a}\:{polynomial}\:{gives}\:{a}\:{remainder} \\ $$$${of}\:−{x}−\mathrm{1}\:{when}\:{divided}\:{by}\:{x}^{\mathrm{2}.} \\ $$$${and}\:\:{a}\:{remainder}\:{of}\:−\mathrm{1}\:{when}\: \\ $$$${divided}\:{by}\:{x}−\mathrm{1}\:.\:{what}\:{is}\:{the}\: \\ $$$${remainder}\:{when}\:{the}\:{polynomial} \\ $$$${divided}\:{by}\:{x}^{\mathrm{2}} \left({x}−\mathrm{1}\right)\:? \\ $$

Question Number 82519 Answers: 1 Comments: 1

Question Number 82489 Answers: 1 Comments: 0

If a^b =b^a and a=2b then find the value of a^2 +b^2 .

$$ \\ $$$$\: \\ $$$$\mathrm{If}\:\mathrm{a}^{\mathrm{b}} =\mathrm{b}^{\mathrm{a}} \:\mathrm{and}\:\mathrm{a}=\mathrm{2b}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:. \\ $$

Question Number 82431 Answers: 1 Comments: 5

Question Number 82404 Answers: 1 Comments: 7

Question Number 82397 Answers: 0 Comments: 2

Question Number 82375 Answers: 2 Comments: 0

if x+y=8 ,,x,y∈R^+ prove that (x+(1/y))^2 +(y+(1/x))^2 ≥((289)/8)

$${if}\:\:{x}+{y}=\mathrm{8}\:\:\:\:\:,,{x},{y}\in\mathbb{R}^{+} \\ $$$${prove}\:{that}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} +\left({y}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \geqslant\frac{\mathrm{289}}{\mathrm{8}} \\ $$

Question Number 82356 Answers: 0 Comments: 1

Question Number 82307 Answers: 0 Comments: 3

Question Number 82274 Answers: 0 Comments: 0

Question Number 82265 Answers: 2 Comments: 0

factorize: (x+1)(x+2)(x+3)(x+6)−3x^2

$${f}\boldsymbol{{actorize}}: \\ $$$$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{6}\right)−\mathrm{3}{x}^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 82191 Answers: 1 Comments: 19

find the solution (√(x^2 −3x−4 )) > x−2

$${find}\:{the}\:{solution} \\ $$$$\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\:}\:\:>\:\:{x}−\mathrm{2}\: \\ $$

Question Number 82149 Answers: 1 Comments: 1

Evaluate the greatest coefficient of (7 − 5x)^(− 3)

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{of}\:\:\:\:\left(\mathrm{7}\:−\:\mathrm{5x}\right)^{−\:\mathrm{3}} \\ $$

Question Number 82082 Answers: 0 Comments: 4

Evaluate: (((√(30 + (√8) + (√5)))/((√8) + (√5))))^(1/4)

$$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$

Question Number 82073 Answers: 1 Comments: 3

Show that: j_(3/2) (x) = ((√2)/(πx)) (((sin x)/x) − cos x)

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\mathrm{j}_{\mathrm{3}/\mathrm{2}} \left(\mathrm{x}\right)\:\:=\:\:\frac{\sqrt{\mathrm{2}}}{\pi\mathrm{x}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:−\:\mathrm{cos}\:\mathrm{x}\right) \\ $$

Question Number 82071 Answers: 2 Comments: 0

x≠ y ≠z ≠ 0 xy + xz + yz = 0 prove that ((x+y)/z)+((x+z)/y)+((y+z)/x) = −3

$${x}\neq\:{y}\:\neq{z}\:\neq\:\mathrm{0} \\ $$$${xy}\:+\:{xz}\:+\:{yz}\:=\:\mathrm{0} \\ $$$${prove}\:{that}\:\frac{{x}+{y}}{{z}}+\frac{{x}+{z}}{{y}}+\frac{{y}+{z}}{{x}}\:=\:−\mathrm{3} \\ $$$$ \\ $$

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