InterviewSolution
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InterviewSolution
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If a+ b + c = 0, then the value of \(\frac{1}{{{b^2} + {c^2} - {a^2}}} + \frac{1}{{{c^2} + {a^2} - {b^2}}} + \frac{1}{{{a^2} + {b^2} - {c^2}}}\) is1. 32. 03. 14. None of the above |
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Answer» Correct Answer - Option 2 : 0 Given a + b + c = 0 Formula used (a + b)2 = a2 + b2 + 2ab Calculation a + b + c = 0 ⇒ a + b = -c On squaring both sides, we get (a + b)2 = c2 ⇒ a2 + b2 + 2ab = c2 ⇒ a2 + b2 - c2 = -2ab ______(1) Similarly, b2 + c2 - a2 = -2bc _____(2) And c2 + a2 - b2 = -2ca _____(3) Then using equation (1), (2) and (3) \(\Rightarrow \frac{1}{{{b^2} + {c^2} - {a^2}}} + \frac{1}{{{c^2} + {a^2} - {b^2}}} + \frac{1}{{{a^2} + {b^2} - {c^2}}} = {1 \over -2bc} + {1 \over -2ca} + {1 \over -2ab}\) \(\Rightarrow {-1 \over 2}({1 \over bc} + {1 \over ca} + {1 \over ab})\) \(\Rightarrow {-1 \over 2}({a + b + c \over abc}) = 0\) |
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