Question

If a+b+c=10 & a^2+b^2+c^2=30 find ab+bc+ca

Answer 1

For this, first we have to be familiar with the identity given below:

$\Large (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$

We are given,

$1.\ \ a+b+c=10\\ \\ 2.\ \ a^2+b^2+c^2=30$

So,

$\begin{aligned}&(a+b+c)^2=10^2\\ \\ \Longrightarrow\ \ &a^2+b^2+c^2+2(ab+bc+ca)=100\\ \\ \Longrightarrow\ \ &30+2(ab+bc+ca)=100\\ \\ \Longrightarrow\ \ &2(ab+bc+ca)=70\\ \\ \Longrightarrow\ \ &ab+bc+ca=\textbf{35}\end{aligned}$

We had to find ab + bc + ca.

Hence the answer is 35.

Answer 2

Answer:

Step-by-step explanation:

I hope u understand

.