Mathematics
If a + b - c = 5 and a2 + b2 + c2 = 29, find the value of ab - bc - ca.
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Answer
Given, a + b - c = 5. Squaring both sides we get,
⇒ (a + b - c)2 = 52
⇒ a2 + b2 + c2 + 2ab - 2bc - 2ca = 25
Substituting values we get,
⇒ 29 + 2(ab - bc - ca) = 25
⇒ 2(ab - bc - ca) = 25 - 29
⇒ 2(ab - bc - ca) = -4
⇒ (ab - bc - ca) = -2.
Hence, (ab - bc - ca) = -2.
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