Question

If a2+b2+c2=85 and ab+bc+ca=3 then find the value of a+b+c

Answer 1

Answer:

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Step by step solution:

$Given \ a^{2} +b^{2} +c^{2}=85\\ \\and \ (ab+bc+ca)=3\\\\We \ have \ to \ find \ (a+b+c)\\\\First \ multiply \ by \ 2 \ in \ (ab+bc+ca)=3\\\\2 (ab+bc+ca)=3 \times2\\\\2 (ab+bc+ca)=3=6\\\\we \ know \ formula\\(a+b+c)^{2}=a^{2} +b^{2} +c^{2}+2(ab+bc+ca)\\\\putting \ value \ here\\\\(a+b+c)^{2}=85+6\\\\(a+b+c)^{2}=91\\\\(a+b+c)=\sqrt{91}$

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