Question Text
Question 4 :
If $\displaystyle 2 \left ( x^{2} + 1 \right ) = 5x$, find $\displaystyle x^{3} - \dfrac{1}{x^{3}}$<br/>
Question 9 :
If $\displaystyle a + \dfrac{1}{a} = 4$ and $\displaystyle a \neq 0$, find :<br/>$\displaystyle a^{4} + \dfrac{1}{a^{4}}$
Question 11 :
If $x+y=a $ and $xy=b$, then the value of $\displaystyle \frac{1}{x^{3}}+\frac{1}{y^{3}} $ is
Question 14 :
Given the polynomial $a_{0}x^{n} + a_{1}x^{n - 1} + ... + a_{n - 1}x + a_{n}$, where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a's$ are integers or zero. Set$h = n + a_{0} + |a_{1}| + |a_{2}| + .... + |a_{n}|$. The number of polynomials with $h = 3$ is
Question 15 :
The value of$\displaystyle \left ( x-y \right )^{3}+\left ( x+y \right )^{3}+3\left ( x-y \right )^{2}\left ( x+y \right )+3\left ( x+y \right )^{2}\left ( x-y \right )$ is
Question 17 :
Two numbers are such that their sum multiplied by the sum of their squares is $5500$ and their difference multiplied by the difference of the squares is $352$. Then the numbers are ?<br/>