Question

Ex.3. If a + b + c = 2s, then (s-a)²+(s – b)² +(s-c)² +52 al + b2 +c2 (1) a² +b +2 (2) 0 (3) 1 (4) 2 is equal to

11th - 12th Class

Maths

Solution

116

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sol. (3) Expression [ begin{array}{c} frac{(s-a)^{2}+(s-b)^{2}+(s-c)^{2}+s^{2}}{a^{2}+b^{2}+c^{2}} =frac{s^{2}-2 s a+a^{2}+s^{2}+b^{2}-2 b s+s^{2}+c^{2}-2 c s+s^{2}}{a^{2}+b^{2}+c^{2}} =frac{4 s^{2}+a^{2}+b^{2}+c^{2}-2 s(a+b+c)}{a^{2}+b^{2}+c^{2}} =frac{4 s^{2}+a^{2}+b^{2}+c^{2}-4 s^{2}}{a^{2}+b^{2}+c^{2}}=1 end{array} ]