If x ^ 2 + y ^ 2 = 4, then the minimum value of x ^ 2 + 2Y is

Given x ^ 2 + y ^ 2 = 4, then: X & # 178; = 4-y & # 178;
So:
x²+2y=4-y²+2y=5-(y²-2y+1)=5-(y-1)²
According to the meaning of the title: - 2 ≤ y ≤ 2
So when y = - 2, the minimum value of (Y-1) &# 178; is - 9, and the minimum value of X & # 178; + 2Y is - 4

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