Question
if a2 + b2 +
c2Â =Â 2(4a -5b -9c)-122 , then a-b-c = ?Solution
a2 + b2 + c2 = 2(4a -5b -9c)-122 So a2 + b2 + c2 -2×4a +2 ×5b + 2×9c +122 = 0 a2 -2×4a +16 + b2 +2 ×5b+25 +c2 +2×9c+81 = 0 So (a-4)2 +(b+5)2+(c+9)2 = 0 As we know that if x2 + y2 +z2 = 0 then x=y=z = 0 So here a-4 = 0 so a =4; b +5 = 0 so b = -5 And c+9 =0 so c = -9 So now a-b-c = 4-(-5)-(-9) = 4+5+9 = 18
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