Question

Given that (a+b)^2 =189 and 6ab = 78, calculate the value of 3(a^2+b^2).

Answer 1

3(a² + b² ) = 489

Explanation:

given

(a + b)² = 189 ← expand left side using FOIL

a² + 2ab + b² = 189 → (1)

given 6ab = 78 ( divide both sides by 3 )

2ab = 26

substitute 2ab = 26 into (1)

a² + 26 + b² = 189 ( subtract 26 from both sides )

a² + b² = 163

then

3(a² + b² ) = 3 × 163 = 489