ALGEBRA 3

If (a - b)² = 30; and a² + b² = 50 find the value of ab.

solution

(a - b)² = 30

(a - b)(a - b) = 30

a(a - b) - b(a - b)  = 30

a² - ab - ab + b²  = 30.

a² - 2ab + b²  = 30.

a² + b² - 2ab = 30.

                   But  a² + b² = 50

50 - 2ab = 30.

50 -  30 = 2ab

20 = 2ab

¹⁰20 =   ¹2ab

    ₁2       ₁2

ab = 10

Hence ab = 10

TRY THIS...............

If (a - b)² = 40; and a² + b² = 110 find the value of ab.