Question

If ab+bc+ca =36 and a2+b2+c2=85 then find a+b+c

Answer 1

(a+b+c)² = a²+b²+c²+2ab+2bc+2ac
(a+b+c)² = 85 + 2(ab+bc+ac)
(a+b+c)² = 85 + 2(36)
(a+b+c)² = 157
a+b+c = 12. 5299640861

Answer 2

Answer:

The value of the expression is $a+b+c=12.52$

Step-by-step explanation:

Given : If ab+bc+ca =36 and $a^2+b^2+c^2=85$

To find : The value of a+b+c ?

Solution :

We know the identity,

$(a+b+c)^2= a^2+b^2+c^2+2ab+2bc+2ac$

$(a+b+c)^2= a^2+b^2+c^2+2(ab+bc+ac)$

Substitute the given values,

$(a+b+c)^2= 85+2(36)$

$(a+b+c)^2= 85+72$

$(a+b+c)^2= 157$

$a+b+c= \sqrt{157}$

$a+b+c=12.52$

Therefore, The value of the expression is $a+b+c=12.52$