Question
If x = 555, y = 554, z = 556, then the value of
x2 + y2 + z2 - xy-yz-zx?Solution
x^2 + y^2 + z^2 - xy-yz-zx = 1/2 {(x-y)^2+(y-z)^2+(z-x)^2 } = 1/2 {(555-554)^2+(554-556)^2+(556-555)^2 } = 1/2 {(1)^2+(-2)^2+(1)^2 } = 1/2 (1 + 4 + 1) = 1/2 × 6 = 3 Alternate method: x^2 + y^2 + z^2 - xy-yz-zx = x(x –y) +y (y – z ) + z (z – x ) = 555(555-554) +554(554-556)+556(556-555) = 555(1)+554(-2)+556(1) =555-554-554+556= 1 +2 = 3
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