$$\frac{{m - {a^2}}}{{{b^2} + {c^2}}}$$ + $$\frac{{m - {b^2}}}{{{c^2} + {a^2}}}$$ + $$\frac{{m - {c^2}}}{{{a^2} + {b^2}}}$$ = 3, then the value of m is?
A. a2 + b2
B. a2 + b2 + c2
C. a2 - b2 - c2
D. a2 + b2 - c2
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \frac{{m - {a^2}}}{{{b^2} + {c^2}}} + \frac{{m - {b^2}}}{{{c^2} + {a^2}}} + \frac{{m - {c^2}}}{{{a^2} + {b^2}}} = 3 \cr & \Rightarrow m = ? \cr & \Rightarrow \frac{{m - {a^2}}}{{{b^2} + {c^2}}} + \frac{{m - {b^2}}}{{{c^2} + {a^2}}} + \frac{{m - {c^2}}}{{{a^2} + {b^2}}} = 1 + 1 + 1 \cr & {\text{Put }}m = {a^2} + {b^2} + {c^2}{\text{ from option (B)}} \cr} $$$${\text{L}}{\text{.H}}{\text{.S}}{\text{. = }}\frac{{{a^2} + {b^2} + {c^2} - {a^2}}}{{{b^2} + {c^2}}} + $$ $$\frac{{{a^2} + {b^2} + {c^2} - {b^2}}}{{{c^2} + {a^2}}} + $$ $$\frac{{{a^2} + {b^2} + {c^2} - {c^2}}}{{{a^2} + {b^2}}}$$
$$\eqalign{ & \Rightarrow \frac{{{b^2} + {c^2}}}{{{b^2} + {c^2}}} + \frac{{{a^2} + {c^2}}}{{{c^2} + {a^2}}} + \frac{{{a^2} + {b^2}}}{{{a^2} + {b^2}}} \cr & \Rightarrow 1 + 1 + 1 = {\text{R}}{\text{.H}}{\text{.S}}{\text{.}} \cr & \Rightarrow m = {a^2} + {b^2} + {c^2} \cr} $$
Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
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D. $$\frac{8}{6}$$
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