Question

Find y^2 + 1/y^2 and y ^4 + 1/y^4 if y-1/y=9.

Answer 1

y-1/y=9
(y-1/y)² = y² + (1/y)² - 2
(9)²+2 = y² + (1/y)²= 83


(y²+1/y²) = y^4+1/y^4+2
(83)²=y^4+1/y^4+2
y^4+1/y^4=6889-2
y^4+1/y^4=6887
if i helped then say thanx and mark my answer as best if it is

Answer 2

You've got $y-\frac{1}{y} = 9$.
Square it, $y^{2}+\frac{1}{y^2}-2=81 \Rightarrow y^{2}+\frac{1}{y^2}=83$.
Raise the power to four, [tex]y^4 - 4y^2 + 6 - 4\frac{1}{y^2} + \frac{1}{y^4} = 6561 \\ \Rightarrow y^4 + \frac{1}{y^4} + 6 - 4(83) =6561 \\ \Rightarrow y^4 + \frac{1}{y^4} = 6887.[/tex]