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AlgebraQuestion and Answers: Page 240

Question Number 101056 Answers: 5 Comments: 1

If the equation 4x^2 −4(5x+1)+p^2 =0 has one root equals to two more then the other, then the value of p is equal to ___

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}\left(\mathrm{5}{x}+\mathrm{1}\right)+{p}^{\mathrm{2}} =\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equals}\:\mathrm{to}\:\mathrm{two}\:\mathrm{more} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{other},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_ \\ $$

Question Number 101052 Answers: 2 Comments: 0

Given a=^3 (√(7+(√(50)))),b=^3 (√(7−(√(50)))).Prove that a^7 +b^7 is an even number.

$$\mathrm{Given}\:\mathrm{a}=\:^{\mathrm{3}} \sqrt{\mathrm{7}+\sqrt{\mathrm{50}}},\mathrm{b}=\:^{\mathrm{3}} \sqrt{\mathrm{7}−\sqrt{\mathrm{50}}}.\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{7}} +\mathrm{b}^{\mathrm{7}} \mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{number}. \\ $$

Question Number 100976 Answers: 0 Comments: 1

find all possible values of x,y,z in terms of a,b,c gor a triplet (x,y,z) that satisfy x+(1/y)=a y+(1/z)=b z+(1/x)=c

$${find}\:{all}\:{possible}\:{values}\:{of}\:{x},{y},{z}\:{in}\:{terms} \\ $$$${of}\:{a},{b},{c}\:{gor}\:{a}\:{triplet}\:\left({x},{y},{z}\right)\:{that}\:{satisfy} \\ $$$$ \\ $$$${x}+\frac{\mathrm{1}}{{y}}={a} \\ $$$$ \\ $$$${y}+\frac{\mathrm{1}}{{z}}={b} \\ $$$$ \\ $$$${z}+\frac{\mathrm{1}}{{x}}={c} \\ $$

Question Number 100960 Answers: 0 Comments: 1

{ (((√(x^2 −6x+9)) = 3−x)),(((√(x^2 +6x+9)) = x+3)) :}

$$\begin{cases}{\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}}\:=\:\mathrm{3}−{x}}\\{\sqrt{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{9}}\:=\:{x}+\mathrm{3}}\end{cases}\: \\ $$

Question Number 100954 Answers: 2 Comments: 1

{ (((1/(2x−y)) + (√y) = 1)),((((√y)/(2x−y)) = −6)) :}

$$\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}\:+\:\sqrt{{y}}\:=\:\mathrm{1}}\\{\frac{\sqrt{{y}}}{\mathrm{2}{x}−{y}}\:=\:−\mathrm{6}}\end{cases} \\ $$

Question Number 100879 Answers: 2 Comments: 1

Solve the equation 2^x +8x=4

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{2}^{\mathrm{x}} +\mathrm{8x}=\mathrm{4} \\ $$

Question Number 100815 Answers: 1 Comments: 0

Question Number 100806 Answers: 1 Comments: 3

Question Number 100793 Answers: 1 Comments: 1

Question Number 100792 Answers: 1 Comments: 0

Question Number 100730 Answers: 0 Comments: 1

((2z^2 )/(z^2 +∣z+1∣)) < 1

$$\frac{\mathrm{2}{z}^{\mathrm{2}} }{{z}^{\mathrm{2}} +\mid{z}+\mathrm{1}\mid}\:<\:\mathrm{1}\: \\ $$

Question Number 100703 Answers: 0 Comments: 2

Question Number 100908 Answers: 2 Comments: 2

what the value of angle formed by a long needle and short needle on analog clock that shows at 15.50 ? (A) 175^o (B) 174^o (C) 173^o (D) 172^o (E) 170^o

$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{angle} \\ $$$$\mathrm{formed}\:\mathrm{by}\:\mathrm{a}\:\mathrm{long}\:\mathrm{needle}\:\mathrm{and}\: \\ $$$$\mathrm{short}\:\mathrm{needle}\:\mathrm{on}\:\mathrm{analog}\:\mathrm{clock}\: \\ $$$$\mathrm{that}\:\mathrm{shows}\:\mathrm{at}\:\mathrm{15}.\mathrm{50}\:? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{175}^{\mathrm{o}} \:\:\:\left(\mathrm{B}\right)\:\mathrm{174}^{\mathrm{o}} \:\:\:\left(\mathrm{C}\right)\:\mathrm{173}^{\mathrm{o}} \\ $$$$\left(\mathrm{D}\right)\:\mathrm{172}^{\mathrm{o}} \:\:\:\:\left(\mathrm{E}\right)\:\mathrm{170}^{\mathrm{o}} \\ $$

Question Number 100660 Answers: 0 Comments: 1

∣x^2 −x∣ < 2+x . find solution set.

$$\mid{x}^{\mathrm{2}} −{x}\mid\:<\:\mathrm{2}+{x}\:.\:{find}\:{solution}\:{set}. \\ $$

Question Number 100622 Answers: 0 Comments: 2

Question Number 100597 Answers: 2 Comments: 1

Question Number 100587 Answers: 2 Comments: 1

If the coefficients of x^k and x^(k+1) in the expansion (2+3x)^(19) are equal , what is the value of k ?

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{of}\:{x}^{{k}} \:\mathrm{and}\:{x}^{{k}+\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{expansion}\:\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{19}} \:\mathrm{are}\:\mathrm{equal}\:,\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:? \\ $$

Question Number 100567 Answers: 0 Comments: 3

{ ((x−(√(yz)) = 42)),((y−(√(xz)) = 6)),((z−(√(xy)) = −30)) :} find x+y+z =

$$\begin{cases}{{x}−\sqrt{{yz}}\:=\:\mathrm{42}}\\{{y}−\sqrt{{xz}}\:=\:\mathrm{6}}\\{{z}−\sqrt{{xy}}\:=\:−\mathrm{30}}\end{cases} \\ $$$${find}\:{x}+{y}+{z}\:= \\ $$

Question Number 100562 Answers: 0 Comments: 0

Question Number 100540 Answers: 0 Comments: 1

Question Number 100492 Answers: 2 Comments: 3

((16−((64)/(16−((64)/(16−((64)/(16−...))))))))^(1/(3 )) −((−2−(1/(−2−(1/(−2−(1/(−2−...))))))))^(1/(3 ))

$$\sqrt[{\mathrm{3}\:\:\:}]{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−...}}}}−\sqrt[{\mathrm{3}\:\:}]{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−...}}}} \\ $$

Question Number 100404 Answers: 0 Comments: 11

Question Number 100385 Answers: 1 Comments: 2

find the solution set of inequality (((x^2 −9)(√(x+2)))/(x+(√((x+2)^2 )))) ≤ 0

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequality} \\ $$$$\frac{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)\sqrt{\mathrm{x}+\mathrm{2}}}{\mathrm{x}+\sqrt{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} }}\:\leqslant\:\mathrm{0} \\ $$

Question Number 100330 Answers: 0 Comments: 1

Question Number 100370 Answers: 1 Comments: 2

Find the maximum value of f(x) = (3/(2cosh (ln x) + 3))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2cosh}\:\left(\mathrm{ln}\:{x}\right)\:+\:\mathrm{3}} \\ $$

Question Number 100302 Answers: 0 Comments: 2

(√(3^(−(1/2)) +1)) = ((√(a+1))/3^(−(1/4)) ) . find a ?

$$\sqrt{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{1}}\:=\:\frac{\sqrt{\mathrm{a}+\mathrm{1}}}{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{4}}} }\:.\:\mathrm{find}\:\mathrm{a}\:? \\ $$

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