Question

If a+b+c = 9 and ab + bc + ca = 40, then find a² + b² +c²​

Answer 1

Answer:

hy

Step-by-step explanation:

Given, a + b + c = 9 and ab + bc + ca = 40

We know that,

(a + b + c)2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca

⇒ a 2 + b 2 + c 2 = (a + b + c)2 – 2 (ab + bc + ca)

⇒ a 2 + b 2 + c 2 = (9)2 – 2 × 40 = 81 – 80 = 1 [a + b + c = 9 and ab + bc + ca = 40]

Thus, the value of a 2 + b 2 + c2 is 1 .

Answer 2

Answer:

1

Step-by-step explanation:

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

9^2 = a^2 + b^2 + c^2 + 2( 40 )

81 = a^2 + b^2 + c^2 + 80

a^2 + b^2 + c^2 = 81 - 80

a^2 + b^2 + c^2 = 1