Question

If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2? a) 46 b)35 c) 81 d) None of these​

Answer 1

Answer:

Step-by-step explanation:

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

81=a2+b2+c2+2(23)

a2+b2+c2=81-46=35

option b is correct

Answer 2

• a+b+c=9
• ab+bc+ca=23

We know

$\boxed{\sf (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca}$

$\\ \sf\longmapsto a+b+c=9$

$\\ \sf\longmapsto (a+b+c)^2=9^2$

$\\ \sf\longmapsto a^2+b^2+c^2+2ab+2bc+2ca=81$

$\\ \sf\longmapsto a^2+b^2+c^2+2(ab+bc+ca)=81$

$\\ \sf\longmapsto a^2+b^2+c^2+2(23)=81$

$\\ \sf\longmapsto a^2+b^2+c^2+46=81$

$\\ \sf\longmapsto a^2+b^2+c^2=81-46$

$\\ \sf\longmapsto a^2+b^2+c^2=35$