Question

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

Solution: using ide​

Answer 1

Using the identity,

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

Given that,

a²+b²+c²=90

and, a+b+c=20

Substituting the appropriate values,

20²=90+2(ab+bc+ca)

→2(ab+bc+ca)=400-90

→2(ab+bc+ca)=310

→ab+bc+ca=155

•The required value is 155.

Verification:

Now,

ab+bc+ca=155 and a²+b²+c²=90

Putting the values,

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

→(a+b+c)²=90+2(155)

→(a+b+c)²=400

→a+b+c=20

Hence, verified

Answer 2

Answer:155

Step-by-step explanation:

(A+b+c)²=a²+b²+c²+2ab+2bc+2ca

(20)²=90+2(ab+bc+ca)

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

310/2=ab+bc+ca

155=ab+bc+ca