Question

if y+ 1/y = -2, then y^50 + 1/y^50 is ?

Answer 1

Refer the attachment for your answer.

Answer 2

Given : $y+\frac{1}{y}=-2$.

We have to find the value of $y^{50}+\frac{1}{y^{50}}$

The given equation can be solved as :

$\begin{array}{l}y+\frac{1}{y}=-2 \\y^{2}+1=-2 y \\y^{2}+2 y+1=0 \\(y)^{2}+2(y)(1)+1=0 \\(y+1)^{2}=0 \\y=-1\end{array}$

$\begin{array}{l}\Rightarrow y^{50}+\frac{1}{y^{50}} \\\Rightarrow(-1)^{50}+\frac{1}{(-1)^{50}} \\=1+\frac{1}{1}\end{array}$

= 1 +1

=2

Hence the value is 2.