Question
If 2x + 4y - 9 = 0, then find the value of 8x 3
- 723 + 64y 3 + 216xy.Solution
2x + 4y - 9 = 0
If, a + b - c = 0, then, a 3 + b 3 - c 3 = - 3abc
So, (2x) 3 + (4y) 3 + ( - 9) 3 = - 3 X (2x) X (4y) X (9)
Or, 8x 3 + 64y 3 - 729 = - 216xy
Or, 8x 3 + 64y 3 - 729 + 216xy = 0 ....(i)
8x 3 - 723 + 64y 3 + 216xy = 8x 3 - 729 + 6 + 64y 3 + 216xy
Put the value of equation (i) in the above equation, we get,
8x 3 - 723 + 64y 3 + 216xy = 0 + 6 = 6
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