Question
If 125x3 - 64y3 = (Ax + By)
(Dy2 - Cx2 + 20xy) , then the value of A + C - 2B + 3D is:Solution
125x3 - 64y3 = (Ax + By) (Dy2 - Cx2 + 20xy)
(5x) 3 - (4y) 3 = (Ax + By) (Dy2 - Cx2 + 20xy)
As we know,
x3 - y3 = (x - y) (x2 + y2 + xy)
So, (5x) 3 - (4y) 3 = (5x - 4y) (25x2 + 16y2 + 20xy) = (Ax + By) (Dy2 - Cx2 + 12xy)
Comparing the coefficients of both sides, we get;
'A' = 5, B = - 4, C = - 25, D = 16
So, A + C - 2B + 3D = 5 - 25 - {2 X ( - 4) } + 3 X 16
= - 20 + 8 + 48 = 36
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