If x + y = 4, find the value of x3 + y3 + 12xy - 64
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Using (x + y)3 = x3 + y3 + 3(x)(y)(x + y)
Putting x + y = 4 in above:
x3 + y3 + 3xy(4) = (4)3
⇒ x3 + y3 + 12xy = 64
⇒ x3 + y3 + 12xy - 64 = 0
∴ Value of x3 + y3 + 12xy - 64 = 0
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If x + 2y - 3 = 0, then find the value of x3 + 8y3 + 6x2y + 12xy2 - 125.
Without actually calculating the cubes, find the values of:
(i) (27)3 + (-17)3 + (-10)3
(ii) (-28)3 + (15)3 + (13)3