If a + b + c = 2, a2 + b2 + c2 = 26, then the value of a3 + b3 + c3 – 3abc is:
Show answer & explanation
Correct answer: A
Explanation
Correct answer is option 1 i.e. 74
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Concept |
Understanding |
Application |
Fair calculation |
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(a+b+c)2 = a2+b2+c2+2(ab+ bc +ca)
a3+b3 + c3- 3abc = (a+b+c)[a2+b2+c2-ab-bc-ca] |
a + b + c = 2 a2 + b2 + c2 = 26 |
4 = 26 + 2(ab+ bc +ca) (ab+ bc +ca) = -11
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(4 – 26)/2 = -11 |
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a3 + b3 + c3 – 3abc = 2 (26 – (-11)) = 74 |
2 × 37 = 74 |