Question

If a2 + b2 + c2 = 90 & a + b + c = 20. Find the value of ab + bc + ca?​

Answer 1

Answer:

Okay So I am just considering that you meant a²+b²+c²= 90

So we have an identity which states that,  

                            (a + b + c)² = a² + b² +c² + 2(ab+ bc + ca)

In the question it is given that a² + b ²+ c² =90, and , a+ b+ c =20.

So just by using the identity mentioned above, I can write,

(a+b+c)² = a²+ b² +c² +2(ab+bc+ca)

⇒ (20)² = 90 + 2(ab +bc +ca)

⇒400 - 90 =2( ab +bc +ca)

⇒310/2 =ab +bc+ ca

⇒155 = ab +bc+ca

Thus, you answer is 155.

Hope my answer helped :-)

Answer 2

Answer:

Ans. 155

Step-by-step explanation:

Given,

a^2+ b^2 +c^2=90;

a+b+c=20

Now,

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

or, (20)^2 = 90 +2(ab+bc+ca)

or, 400= 90+2(ab+bc+ca)

or, 2(ab+bc+ca)=400-90

or, 2(ab+bc+ca) = 310

or, ab+bc+ca = 155 Ans.