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Minimum

Let \(x,y,z\geq-1\) be real numbers satisfying \(xy+yz+zx+xyz=2\). Find the minimum value of \((1+x)(1+y)(1+z)\) and prove that it is the minimum.

Note by Yan Yau Cheng
3 years, 6 months ago

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The minimum value of (1 + x)(1 + y)(1 + z) would be when x, y, or z are minimum. However, to satisfy the first equation, x = y = z = -1, because it would yield the equation as 2. Thus, the minimum value of (1 + x)(1 + y)(1 + z) is 0

Nanayaranaraknas Vahdam - 3 years, 6 months ago

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Vishal Sharma - 3 years, 6 months ago

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