Question

Find $y^2+\frac{1}{y^2}$ and $y^4+\frac{1}{y^4}$ if $y+\frac{1}{y}=9$

Answer 1

$y+\frac{1}{y}=9$

Squaring both side

${(y+\frac{1}{y})}^2=9^2$

$y^2+\frac{1}{y^2}+2\times y\times \frac{1}{y}=81$

$y^2+\frac{1}{y^2}=81-2=79$

Squaring

${(y^2+\frac{1}{y^2})}^2=(79{)}^2$

$y^4+\frac{1}{y^4}+2\times y^2\times \frac{1}{y^2}=6241$

$y^4+\frac{1}{y^4}=6,239$.