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Question Number 74209 by FCB last updated on 20/Nov/19

	Answered by mind is power last updated on 20/Nov/19

	$a^{2} + b^{2} + c^{2} = 48$ $a ⩾ b ⩾ c$ $\Rightarrow 48 ⩾ 3 a^{2} \Rightarrow a^{2} ⩽ 16 \Rightarrow a ⩽ 4$ $a = 4 \Rightarrow b^{2} + c^{2} = 32 \Rightarrow (b, c) = (4, 4)$ $a = 3 \Rightarrow b^{2} + c^{2} = 39 n o n s o l u t i o n$ $a = 2 \Rightarrow b^{2} + c^{2} = 44 \Rightarrow n o n s o l u t i o n$ $a = 1 \Rightarrow b^{2} + c^{2} = 47 \Rightarrow n o n s o l u t i o n$ $a = 0 \Rightarrow b^{2} + c^{2} = 48 \Rightarrow n o n s o l u t i o n$ $\Rightarrow (a, b, c) = (4, 4, 4)$ $o u r e x p r e s s i o n = 3.16 . \sqrt{144} = 3.16.12 = 576$
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