Question

if a+b+c=9 and ab+bc+ca=14 find a​

Answer 1

Answer:

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