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AlgebraQuestion and Answers: Page 277

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

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

Question Number 82041 Answers: 1 Comments: 4

show that π^(ie) +(1/2)=0

$${show}\:{that} \\ $$$$\pi^{{ie}} +\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$

Question Number 82031 Answers: 1 Comments: 0

find x,y { ((5(√(2x^2 −y^4 )) =4x−3y)),((4(√(2x^2 −y^4 )) =3x−2y)) :}

$${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$

Question Number 82130 Answers: 0 Comments: 5

In an arrangement of the word VIOLENT, find the chances that the vowels I, O, E occupy the odd positions.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{arrangement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{VIOLENT},\:\mathrm{find}\:\mathrm{the}\:\mathrm{chances} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{vowels}\:\:\:\mathrm{I},\:\mathrm{O},\:\mathrm{E}\:\:\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{positions}. \\ $$

Question Number 81944 Answers: 2 Comments: 0

show that cot(40°)−cot(50°)=2tan(10°) cos(70°) cos(50^° ) cos(10^° )=((√3)/8)

$${show}\:{that}\: \\ $$$${cot}\left(\mathrm{40}°\right)−{cot}\left(\mathrm{50}°\right)=\mathrm{2}{tan}\left(\mathrm{10}°\right) \\ $$$${cos}\left(\mathrm{70}°\right)\:{cos}\left(\mathrm{50}^{°} \right)\:{cos}\left(\mathrm{10}^{°} \right)=\frac{\sqrt{\mathrm{3}}}{\mathrm{8}} \\ $$

Question Number 81943 Answers: 0 Comments: 0

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 81942 Answers: 1 Comments: 0

Question Number 81910 Answers: 0 Comments: 1

a_1 =1 a_2 =2 a_(n+1) =(n+1)a_n −2a_(n−1) find a_n =?

$${a}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){a}_{{n}} −\mathrm{2}{a}_{{n}−\mathrm{1}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 81892 Answers: 5 Comments: 0

Question Number 81871 Answers: 1 Comments: 3

a_1 =4 a_(n+1) =((4a_n +3)/(a_n +2)) find a_n =?

$${a}_{\mathrm{1}} =\mathrm{4} \\ $$$${a}_{{n}+\mathrm{1}} =\frac{\mathrm{4}{a}_{{n}} +\mathrm{3}}{{a}_{{n}} +\mathrm{2}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 81821 Answers: 1 Comments: 0

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