Friday 10 April 2015

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.

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