CDS ALGEBRA QUIZ 35

Question 1:

If $4 \cdot x^{9 / 4}-9 \cdot x^{9 / 8}+4=0$, then find $x^{9 / 4}+x^{-9 / 4}=$.

$\frac{53}{20}$

$\frac{64}{33}$

$\frac{49}{16}$

$\frac{9}{4}$

Question 2:

If $\frac{4 p}{p^{2}-4 p+4}=\frac{1}{4}(p \neq 0)$, then find $p^{2}+\frac{16}{p^{2}}$

392

400

398

396

Question 3:

If $\left(a+\frac{1}{a}\right)^{2}-2\left(a-\frac{1}{a}\right)-12=0$ then find the value of $a-\frac{1}{a}$

$(4,-2)$

$-2,-4$

$-3,2$

$(2,3)$

Question 4:

If $16 x^{4}+36 x^{2} y+81 y^{4}=806$ and $4 x^{2}-6 x y+$ $9 y^{2}=26$, then find the value of $4 x y .$

$2.5$

$1.5$

$1.6$

$2.7$

Question 5:

If $x=\sqrt{5}+1$ and $y=\sqrt{5}-1$, then what is the value of $\left(\frac{x^{2}}{y^{2}}\right)+\left(\frac{y^{2}}{x^{2}}\right)+4\left(\frac{x}{y}\right)+4\left(\frac{y}{x}\right)$ $+6 $?

25

49

36

100

Question 6:

If $\ x=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ and $y=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ then find the value of $\frac{x^{2}+x y+y^{2}}{x^{2}-x y+y^{2}}$?

$\frac{67}{65}$

$\frac{63}{61}$

$\frac{65}{62}$

$\frac{69}{71}$

Question 7:

If $x=\sqrt{\sqrt{\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}}}$, then find $x^{8}+\frac{1}{x^{8}}=?$

1156

1154

1152

1158

Question 8:

If $a=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ then $\frac{a^{2}}{b}+\frac{b^{2}}{a}$

900

970

1030

930

Question 9:

If $\frac{2 x}{5 x^{2}-7 x+5}=\frac{1}{3}$, then find the value of $x^{2}+\frac{1}{x^{2}}$.

$\frac{69}{25}$

$\frac{64}{25}$

$\frac{119}{25}$

$\frac{138}{25}$

Question 10:

If $x-\frac{1}{x}=3$, then what is the value of $\frac{2 x^{4}+3 x^{3}+13 x^{2}-3 x+2}{\left(3 x^{4}+3\right)}$

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{4}{3}$

$\frac{5}{3}$