Which one is true?

{ p = 11 + 5 q = 14 + 2 r = 13 + 3 \large \begin{cases} p = \sqrt{11} + \sqrt{5} \\ q = \sqrt{14} +\sqrt{2} \\ r = \sqrt{13} + \sqrt{3} \end{cases}

Given the above, which of the options holds true?

p > q > r p > q > r p < r < q p < r < q p > r > q p > r > q p < q < r p < q < r

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1 solution

Chew-Seong Cheong
Aug 19, 2017

{ p = 11 + 5 p 2 = 16 + 2 55 q = 14 + 2 q 2 = 16 + 2 28 r = 13 + 3 r 2 = 16 + 2 39 p > r > q \begin{cases} p = \sqrt {11} + \sqrt 5 & \implies p^2 = 16 + 2\sqrt{55} \\ q = \sqrt {14} + \sqrt 2 & \implies q^2 = 16 + 2\sqrt{28} \\ r = \sqrt {13} + \sqrt 3 & \implies r^2 = 16 + 2\sqrt{39} \end{cases} \implies \boxed{p>r>q}

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