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Question Number 169977 by infinityaction last updated on 13/May/22

	Answered by ajfour last updated on 13/May/22

	${(a + b + c + d)}^{2} ⩾ 16 \sqrt{a b c d}$ $(a^{2} + b^{2} + c^{2} + d^{2}) ⩾ 4 \sqrt{a b c d}$ $s o s q u a r e o f l . h . s$ $⩾ \frac{16}{144 \times 4} (= \frac{1}{36})$ $a b + b c + c d + d a + a c + b d$ $⩾ 6 \sqrt{a b c d}$ $r . h . s . ⩽ \frac{1}{6}$ $h e n c e p r o v e d, i t h i n k, r e a s o n o u t y o u r s e l f n o w . .$
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