Have this problem in a school maths tutorial

[main hollow]

Been questioning my life's existence for the past hour and a half.

[nova minnow]

Note that $\frac{1}{a^2}+\frac{1}{b^2}=\frac{a^2+b^2}{a^2 b^2}$ \ \ Try and manipulate the numerator to be in terms of $(a-b)^2$ and $ab$.

[shy grail]

Civil Service Pigeon

[faint needle]

(a²+b²)/a²b² = m
(a²+b²)/(ab)² = m
(a²+b²)/k² = m
a²+b² = mk²
a²+b²-2ab = mk²-2k
(a-b)² = mk²-2k

[main hollow]

Thank you so much

[rustic owl]

@main hollow has given 1 rep to @faint needle