Question

if a+b=12, an ab=32 find the value of a²+b²

Answer 1

we know that,

a²+b²= (a+b)²-2ab

let's prove this identity,

RHS

= (a+b)²-2ab

= a²+b²+2ab-2ab

= a²+b²= LHS

Hence proved//

now,

substituting the given values , we have,

12²-2 x 32

= 144-64

= 80

___________________

Answer 2

(a+b)²=12² (because a+b=12)
(a+b)²=a²+2ab+b²
(a+b)²=144
144=a²+b²+2ab
144=a²+b²+2×32
144-64=a²+b²
a²+b²=80