If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of a3 + b3 is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 776
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Understanding Given a + b = 20 and ab = 4 |
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Application (a + b)2 = 202 ⇒ a2 + b2 + 2ab = 400 ⇒ a2 + b2 + 2 × 4 = 400 ⇒ a2 + b2 = 400 - 8 ⇒ a2 + b2 = 392 |
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Now a3 + b3 = (a + b)(a2 + b2 - ab) = 20(392 - 4) = 20 × 388 = 7760 |