If m^2+m^-2=23, then what is the value of m^3+ m^-3?

Question

Your answer

Flame · Answer 1 · 2023-02-20T10:03:25+0000

To find the value of $m^3 + m^{ -3}$ , we can use a clever algebraic manipulation. Let's start by squaring the equation $m^2 + m^{ -2} = 23$ :

$m^2 + m^{ -2})^2 = 23^2$

Expanding the left side of the equation using the binomial theorem:

$m4+2m2⋅m−2+(m−2)2=529m^4 + 2m^2 cdot m^{ -2} + (m^{ -2})^2 = 529$

Simplifying:

$m^4 + 2 + m^{ -4} = 529$