Question

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

Answer 1

Step-by-step explanation:

A²+B²+C²-AB-AC-BC =0

A²+B²+C²=AB+BC+CA

For this to be true, A=B=C

Hence, the ratio will be 1:1:1

I’d suggest you just remember this, you will see a lot of questions based on this in your algebra particularly those that deal with the cube of A+B+C

Answer 2

Answer:

RHS=LHS

Step-by-step explanation:

consider RHS:

=(a+b)²+(b+c)²+(c+a)²

=(a²+b²+2ab)+(b²+c²+2bc)+(c²+a²+2ca)

=a²+a²+b²+b²+c²+c²+2ab+2bc+2ca

=2a²+2b²+2c²+2ab+2bc+2ca

=2(a²+b²+c²+ab+bc+ca)

RHS=LHS

hence proved.

hope the answer is helpful.