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# Inequality on four positive real numbers (TOMATO Subjective 82)

Let a, b, c, d be positive real numbers such that abcd = 1. Show that $$(1+a)(1+b)(1+c)(1+d) \ge 16$$

Discussion:

Concept: Inequality (see this link for some background information).

Using A.M. – G.M. inequality we see that

$$\frac{1+a}{2} \ge \sqrt {1 \times a}$$
$$\frac{1+b}{2} \ge \sqrt {1 \times b}$$

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April 21, 2015

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