EXPONENTIAL EQUATIONS 2

If (a - b)² = 80; and a² + b² = 50 find the value of ab.

solution

(a - b)² = 80

(a - b)(a - b) = 80

a(a - b) - b(a - b)  = 80

a² - ab - ab + b²  = 80.

a² - 2ab + b²  = 80.

a² + b² - 2ab = 80.

                   But  a² + b² = 50

50 - 2ab = 80.

50 -  80 = 2ab

-30 = 2ab

^-15-30 =   ¹2ab

    ₁2       ₁2

ab = -15

Hence ab = -15

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

If (m- n)² = 90; and m² + n² = 140 find the value of mn.