Question

(i) If a +b +c=9 and a2

+ b2

+ c2

=29, find ab +bc + ca.​

Answer 1

Answer:

Given a+b+c=9 and a^2+b^2+c^2=29 then ab+bc+ca=26

Answer 2

Let us examine the following expression:

$a+b+c=9\\\\\implies (a+b+c)^2=81\\\implies \{a+(b+c)\}^2=81\\\\Taking\:b+c=x\right\\\implies(a+x)^2=81\\\implies a^2+x^2+2ax = 81\\\\Putting\:back\:the\:value\:of\:x\\\implies a^2 + (b+c)^2 + 2a(b+c)=81\\\implies a^2 + (b^2 + c^2 + 2bc) + 2ab + 2ca = 81\\\implies a^2 + b^2 + c^2 +2ab+2bc+2ca = 81\\\\Putting\:value\:of\:a^2+b^2+c^2\:(=29)\\\implies 29 + 2(ab+bc+ca)=81\\\implies 2(ab+bc+ca)=81-29\\\implies ab+bc+ca = \frac{52}{2}\\\therefore ab+bc+ca=26$