GATE CSE 2014 Set 1 | Question: GA-4

Question

If $\large\left(z + \dfrac{1}{z}\right)^{2}= 98$, compute $\large \left(z^{2} +\dfrac{1}{z^{2}}\right)$.

Answer 1

$\quad \left(Z+\dfrac{1}{Z}\right)^{2}$

$= \left(z^{2} + 2(z)\left(\dfrac{1}{z}\right) + \left(\dfrac{1}{z}\right)^{2}\right) = \left(z^{2} + \dfrac{1}{z^{2}}\right)+2 =98$

$\Rightarrow 98-2 = 96$ is answer..

Comments

answer is 96

Answer 2

$\left(Z+\dfrac{1}{Z}\right)^{2}=98$

$\implies Z^{2}+\dfrac{1}{Z^{2}}+2Z\cdot \dfrac{1}{Z}=98$

$\implies Z^{2}+\dfrac{1}{Z^{2}}+2=98$

$\implies Z^{2}+\dfrac{1}{Z^{2}}=96$