Question

(x-y)^3=8 so what will the value of (x+y)^2​

Answer 1

${(x - y)}^{3} = 8 \\ {(x - y)}^{3} = {2}^{3} \\ x - y = 2 \\ \\ {(x - y)}^{2} = {2}^{2} = 4$

(x-y)³ = (x-y)(x²+xy+y²) = 8

2(x²+xy+y²) = 8

x²+xy+y² = 4

Since (x-y)² = 4

x²+xy+y² = (x-y)² = 4

x²+xy+y² = x²+y²-2xy

3xy = 0

xy = 0

Therefore,

(x-y)² = 4

x²+y²-2xy =4

x²+y²+0 = 4

x²+y² = 4

(x+y)² = x²+y²+2xy = x²+y² = 4

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