Question

if a square + b square + c square equal to 90 and a + b + c equal to 20 then find the value of a b + BC + CA​

Answer 1

Answer:

$ab + bc + ca = 155 \: ans$

Step-by-step explanation:

Given :

1. ${a}^{2} + {b}^{2} + {c}^{2} = 90$
2. $a+ b + c = 20$

To find :

$ab + bc+ ca = ?$

Solution :

We take,

$a + b + c = 20$

On Squaring both sides :-

${( a+ b + c)}^{2} = {(20)}^{2}$

${a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca = 400$

$90 + 2(ab + bc +ca) = 400 \\ (given \: from \: 1) \\ (taking \: 2 \: as \: common)$

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

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

$ab + bc + ca = \frac{310}{2}$

$ab + bc + ca = 155$