Question
If a 2 + b 2 = 89 and a
2 - b 2 = 39, then find the value of a 3 - b 3 - 3ab, (a, b >0).Solution
a 2 + b 2 = 89 ........ (1)
a 2 - b 2 = 39 ........ (2)
From (1) and (2):
a 2 = 64 => a = 8
b 2 = 25 => b = 5
Now,
a 3 - b 3 - 3ab
= 8 3 - 5 3 - 3 * 8 * 5 = 512 - 125 – 120 = 267
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