If a + b - c = 12 and a2 + b2 + c2 = 110, then which among the following relations is true?
(p) ab + bc + ca = 34
(q) ab + bc - ca = 17
(r) ab - bc + ca = 17
(s) ab - bc - ca = 17
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. s
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Understanding |
Application |
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(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ac |
Given a + b - c = 12 and a2 + b2 + c2 = 110 |
(a + b - c)2 = 12 ⇒ a2 + b2 + c2 + 2ab - 2bc - 2ac = 144 ⇒ 2ab - 2bc - 2ac = 144 – 110 = 34 ⇒ ab - bc - ac = 17 Hence, statement (s) is correct.
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