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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

- 3 years, 6 months ago

0

- 3 years, 6 months ago