Question

24) If a+b+c=9, and ab + bc + ca = 24 find the value of a2+b2+c2​

Answer 1

Answer:

108

Step-by-step explanation:

a+b+c=9 and a

2

+b

2

+c

2

=35

Using formula,

(a+b+c)

2

=a

2

+b

2

+c

2

+2(ab+bc+ca)

9

2

=35+2(ab+bc+ca)

2(ab+bc+ca)=81−35=46

(ab+bc+ca)=23

using formula,

(a

3

+b

3

+c

3

)−3abc=(a

2

+b

2

+c

2

−ab−bc−ca)(a+b+c)

a

3

+b

3

+c

3

−3abc=(35−23)×9=9×12=108