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Question

If $$a^2+b^2+c^2=250$$ and $$ab+bc+ca=3$$, then find $$a+b+c$$.


Solution

$$a^{2}+b^{2}+c^{2}= 250$$ & $$ab+bc+ac= 3$$, find $$a+b+c$$
$$\rightarrow $$ the general formula
$$(a+b+c)^{2}= a^{2}+b^{2}+c^{2}+2(ab+bc+ac)$$
$$= 250+2(3)$$
$$= 250+6$$
$$\therefore (a+b+c)^{2}= 256$$
$$\therefore a+b+c= \sqrt{256}$$
$$\therefore a+b+c= 16$$

1118788_1137388_ans_7dc56e4c544b4368ada022773e2e10b9.jpg

Mathematics

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