R. D. Sharma Solutions for Chapter: Algebraic Identities, Exercise 6: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

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

If $x+\frac{1}{x}=3$, then find the value of $x^6+\frac{1}{x^6}$.

If $a+b=7$ and $ab=12$, find the value of $a^2+b^2$

If $a-b=5$ and $ab=12$, find the value of $a^2+b^2$.

If $x-\frac{1}{x}=\frac{1}{2}$, then write the value of $4x^2+\frac{4}{x^2}$.

If $a^2+\frac{1}{a^2}=102$, then write the positive integer value of $a-\frac{1}{a}$.

If $a+b+c=0$, then write the value of $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$