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Question

If $$a + b + c = 9$$ and $$ab + bc + ca = 26$$, then find $$a^{2} + b^{2} + c^{2}$$.


A
26
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B
27
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C
28
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D
29
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Solution

The correct option is D $$29$$
Given, $$a+b+c=9$$ and $$ab+bc +ca=26$$.

We know, $$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab +2bc+2ca$$
$$\Rightarrow (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$$.

Putting the values here, we get,
$$ (9)^{2}=a^{2}+b^{2}+c^{2}+2(26)$$
$$\Rightarrow 81=a^{2}+b^{2}+c^{2}+52$$
$$\Rightarrow a^{2}+b^{2}+c^{2}=81-52=29$$.

Hence, option $$D$$ is correct.

Mathematics

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