Question

if a square + b square + c square is equal to 74 and AB + BC + CA is equal to 61 find a + b + c ​

Answer 1

$\large\underline\mathfrak{Answer}$

a + b + c = 14

$\large\underline\mathfrak{Explanation}$

$\begin{lgathered}\bold{Given} \begin{cases}\sf{a^2+b^2+c^2=74} \\ \sf{ab+bc+ac=61}\end{cases}\end{lgathered}$

$\bold\red{To\:Find-}$

• Value of (a+b+c)

$\bold\red{Explanation-}$

We know that,

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

Putting the given values,

$\implies$ $\sf{(a+b+c)^2=74+2(61)}$

$\implies$ $\sf{(a+b+c)^2=74+122}$

$\implies$ $\sf{(a+b+c)^2=196}$

$\implies$ $\sf{(a+b+c)=\sqrt{196}}$

$\implies$ $\sf{(a+b+c)=14}$

Hence, the value of (a+b+c) is 14.

$\rule{200}2$

Verification :

Putting the values separately in LHS and RHS,

$\implies$ $\sf{(14)^2=74+2(61)}$

$\implies$ $\sf{196=74+122}$

$\implies$ $\sf{196=196}$

Hence verified!

Answer 2

Step-by-step explanation:

Given

a²+b²+c²=74

ab+bc+ca=61

a+b+c=?

we know that,

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

here we have to put the value

(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

hence:-

the value of (a+b+c)=14