+0  
 
0
91
1
avatar

If , m+(1/m) = 8 then what is the value of m^4 + 1/m^4?

 Jan 9, 2022
 #1
avatar+26 
0

Squaring both sides, we get that \(\left(m + \frac 1m \right)^2 = 8^2\). Expanding gives \(m^2 + \frac{1}{m^2} + 2 = 8^2\), so hence \(m^2 + \frac{1}{m^2} = 8^2 - 2 = 62\). Squaring both sides again, we get that \(\left(m^2 + \frac{1}{m^2}\right)^2 = 62^2\). Expanding gives \(m^4 + \frac{1}{m^4} + 2 = 62^2\), so hence \(m^4 + \frac{1}{m^4} = 62^2 - 2 = \boxed{3842}\).

 Jan 10, 2022

4 Online Users