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If a (a + b + c) = 45; b (a + b + c) = 75 and c ( a + b + c) = 105, then find the value of a² + b² + c².Here is the solution to this problem…..The given equations are:a (a + b + c) = 45 …….(i)b (a + b + c) = 75 ……..(ii)c (a + b + c)= 105 …….(iii)Adding (i), (ii) and (iii), we get:(a + b + c) (a + b + c) =45 + 75 + 105i.e. (a + b + c)^2 = 225Taking square root on both sides of above eqn., we get:(a + b + c) = 15Put the value of (a + b + c) in eqn.s (i), (ii) and (iii), we get:a × 15 = 45b × 15 = 75c × 15 = 105This implies thata = 3, b = 5, c = 7So, we have(a^2 + b^2 + c^2) = 3^2 + 5^2 + 7^2= 9 + 25 + 49=83. :-) |
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