Question

If a² + b2 + c2 = 74 and ab + bc + ac = 61, find a + b + c.​

Answer 1

Correct question :

If a² + b² + c² = 74 and ab + bc + ac = 61, then find a + b + c.

Answer :

value of (a+b+c) is 14

Explanation :

We know that,

(a+b+c)² = a²+b²+c²+2(ab+bc+ac)

Putting the values,

=> (a+b+c)² = 74 + 2(61)

=> (a+b+c)² = 74 + 122

=> (a+b+c)² = 196

=> (a+b+c) = √196

=> a + b + c = 14

Therefore, value of (a+b+c) is 14

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt\bf{GIVEN}}\begin{cases}\sf{{a}^{2}+{b}^{2}+{c}^{2}=74}\\\sf{ab+bc+ac=61} \end{cases}$

$\huge \tt {TO\:FIND:-}$

• a+b+c=?

$\huge \tt {SOLUTION:-}$

We know that,

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

Putting in the values,

$\leadsto\tt {{(a+b+c)}^{2}=74+2 (61)}$

$\leadsto\tt {{(a+b+c)}^{2}=74+122}$

$\leadsto\tt {{(a+b+c)}^{2}=196}$

$\leadsto\tt {a+b+c=\sqrt {196}}$

$\leadsto \huge {\boxed {\tt {a+b+c=14}}}$

$\rule {200}2$