find the value of ab+bc+ca , if a+b+c+=9 and a2 + b2 + c2 =35
Hi!
Given, a + b + c = 9 and a2 + b2 + c2 = 35
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ 2 (ab + bc + ca) = (a + b + c)2 – (a2 + b2 + c2)
⇒ 2 (ab + bc + ca) = (9)2 – 35 = 46 [a + b + c = 9 and a2 + b2 + c2 = 35]
⇒ ab + bc + ca = 23
Thus, the value of ab + bc + ca is 23.
Cheers!