Question

if a+b+c =9 and ab+bc+ca = 27, then
A square+B square+C square= ?

A 35
B 58
C 21
D None of these​

Answer 1

Answer: 27

Step-by-step explanation:

A+B+C=9

AB+BC+CA=27

Using identity (A+B+C)whole square ,

(A+B+C)square = A Square+ B squate +C square + 2AB +2BC +2CA

(A+B+C) square - 2 ( AB + BC + CA) = A square + B square + C square

Put a+b+c =9 and ab + bc +ca =27

(9 )square -2 (27) = A square + B square+ C square

=81-54

=27

Answer 2

Given:-

a+b+c=9

ab+bc+ca=27

To find:-

Value of a²+b²+c²

Solution:-

By squaring both sides in equation,a+b+c=9,we get-----

=>(a+b+c)²=(9)²

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

=>a²+b²+c²+2(ab+bc+ca)=81

=>a²+b²+c²+2(27)=81

=>a²+b²+c²+54=81

=>a²+b²+c²=81-54

=>a²+b²+c²=27

Thus,value of a²+b²+c² is 27.

Hence,correct option is D.