Question

if (a+b)squared=64, and ab=3, find a squared+ b squared

Answer 1

we can also rewrite this (a+b)squared=64 as
(a+b)^2 = 64
first we expand (a+b)^2
(a+b)^2 = 64
(a+b)(a+b) = 64
a^2 + 2ab + b^2 = 64
since we are given the value of ab, which is ab = 3, we can substitute it here:
a^2 + 2(3) + b^2 = 64
a^2 + 6 + b^2 = 64
a^2 + b^2 = 64 - 6
a^2 + b^2 = 58

hope this helps~ :)