Question:
If a2 + 32 + b2 + 8(a + b) = 0, then find the value of (a3 + b3).
If a2 + 32 + b2 + 8(a + b) = 0, then find the value of (a3 + b3).
Updated On: Sep 10, 2024
- -128
- -192
- -124
- -132
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The Correct Option is A
Solution and Explanation
The correct option is (A): -128.
Given, a2 + 32 + b2 + 8(a + b) = 0
Or, a2 + 16 + 8a + b2 + 16 + 8b = 0
Or, (a + 4)2 + (b + 4)2 = 0 (Since, (a + b)2 = a2 + b2 + 2ab)
This can be possible only when both terms are zero
Therefore, (a + 4)2 = 0 and (b + 4)2 = 0
Or, a = b = -4
Therefore, a3 + b3 = (-4)3 + (-4)3 = -64 + (-64) = -128.
Given, a2 + 32 + b2 + 8(a + b) = 0
Or, a2 + 16 + 8a + b2 + 16 + 8b = 0
Or, (a + 4)2 + (b + 4)2 = 0 (Since, (a + b)2 = a2 + b2 + 2ab)
This can be possible only when both terms are zero
Therefore, (a + 4)2 = 0 and (b + 4)2 = 0
Or, a = b = -4
Therefore, a3 + b3 = (-4)3 + (-4)3 = -64 + (-64) = -128.
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