Question

if a²+b²+c² = 90 and a+ b+ c = 20 , then find the value of ab + bc +ca.

Answer 1

Answer:

105

Step-by-step explanation:

We know that $(a+ b+ c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$ (*)

Given a²+b²+c² = 90 and a+ b+ c = 20

So from (*) we can write:

$20^2 = 90 + 2(ab + bc + ca)$

=> 400 - 90 = 2(ab + bc + ca)

=> 2(ab + bc + ca) = 310

=> ab + bc + ca = 310/2

=> ab + bc + ca = 105