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Question
If a + 2b = 5; then show that : a3 + 8b3 + 30ab = 125.
Sum
Solution
Given that a + 2b = 5
We need to find a3 + 8b3 + 30ab
Now consider the cube of a + 2b
( a + 2b )3 = a3 + (2b)3 + 3 × a × 2b × ( a + 2b )
( a + 2b )3 = a3 + 8b3 + 6ab × ( a + 2b )
53 = a3 + 8b3 + 6ab × 5 [ ∵ a + 2b = 5 ]
125 = a3 + 8b3 + 30ab
Thus the value of a3 + 8b3 + 30ab is 125.
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