By using suitable identities, evaluate the following:
(10.1)3
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(10.1)3 = (10 + 0.1)3
Using (a + b)3 = a3 + b3 + 3(a)(b)(a + b),
(10 + 0.1)3 = (10)3 + (0.1)3 + 3(10)(0.1)(10.1)
= 1000 + 0.001 + 30.3
= 1030.301
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(103)3
(99)3
If 2a - b + c = 0, prove 4a2 - b2 + c2 + 4ac = 0
If a + b + 2c = 0, prove that a3 + b3 + 8c3 = 6abc