Given that x, y ∈ R, try to compare the size of X & # 178; + Y & # 178; + 1 and XY + X

Given that x, y ∈ R, try to compare the size of X & # 178; + Y & # 178; + 1 and XY + X

x²+y²+1-(xy+x)
=x²+y²+1-xy-x
=1/2(2x²+2y²+2-2xy-2x)
=1/2(x²-2xy+y²+x²-2x+1+y²)
=1/2[(x-y)²+(x-1)²+y²]>=0
∴x²+y²+1>=(xy+x)

Elden Ring Premiere

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