Question

(c) If a
${a}^{2}$
a2+ b2 + c2 = 50 and ab + bc + ca = 47, find a +b+c.​

Answer 1

Step-by-step explanation:

Given:-

$\\ \sf{:}\longrightarrow a^2+b^2+c^2=50$

$\\ \sf{:}\longrightarrow ab+bc+ca=47$

To find:-

$\\ \sf{:}\longrightarrow a+b+c$

Solution:-

We know that

$\boxed{\boxed{\sf (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca}}$

$\\ \sf{:}\longrightarrow (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$

• Substituting the values Given

$\\ \sf{:}\longrightarrow (a+b+c)^2=50+2(47)$

$\\ \sf{:}\longrightarrow (a+b+c)^2=50+94$

$\\ \sf{:}\longrightarrow (a+b+c)^2=144$

$\\ \sf{:}\longrightarrow a+b+c=\sqrt[2]{144}$

$\\ \sf{:}\longrightarrow a+b+c=12$

$\\ \\ \therefore\sf{a+b+c=12}$