Răspuns:
E(x,y) = 3⁴ = 81
Explicație pas cu pas:
E(x,y) = (x²+2xy)(x²+2xy+2y²)+y⁴
x+y = 3 => E(x,y) = 81 ?
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E(x,y) =x⁴+2x³y+2x²y²+2x³y+4x²y²+4xy³+y⁴ = >
E(x,y) = x⁴+4x³y+6x²y²+4xy³+y⁴ = (x+y)⁴ =>
E(x,y) = 3⁴ = 81
(x+y)⁴ = (x+y)²(x+y)² = (x²+2xy+y²)(x²+2xy+y²) =
= x⁴+2x³y+x²y²+2x³y+4x²y²+2xy³+x²y²+2xy³+y⁴ =
= x⁴+4x³y+6x²y²+4xy³+y⁴
