Question:
If a3 + b3 + c3 = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?
If a3 + b3 + c3 = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?
Updated On: Aug 21, 2024
- 3
- 4
- 5
- 6
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The Correct Option is A
Solution and Explanation
We know, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
52 = a2 + b2 + c2 + 2(ab + bc + ac)
a2 + b2 + c2 = 25 - 2(ab + bc + ac)) …. (i)
a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) + 3abc
62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))
ab + bc + ac = 3
So, the correct option is (A) : 3.
52 = a2 + b2 + c2 + 2(ab + bc + ac)
a2 + b2 + c2 = 25 - 2(ab + bc + ac)) …. (i)
a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) + 3abc
62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))
ab + bc + ac = 3
So, the correct option is (A) : 3.
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