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  • The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

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\\ \text{Let the numbers be} \ a, b$ and $c$ \\ Then, $a^{2}+b^{2}+c^{2}=138$ and $(a b+b c+c a)=131$ \\ $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(a b+b c+c a)=138+2 \times 131=400$ \\ $\Rightarrow(a+b+c)=\sqrt{400}=20$

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Deependra Verma

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