a + b + c = 15 এবং a2 + b2 + c2 = 83 হলে ab + bc + ca = কত ?

a + b + c = 15 এবং a² + b² + c² = 83 হলে ab + bc + ca = কত ?

A 50

B 61

C 71

D 99

Correct Answer: Option C

a+b+c = 15 , a²+b²+c² = 83,

We know that,

2(ab+bc+ca ) = (a+b+c )² - (a²+b²+c² )

or, ab+bc+ca = \(\frac{{(a + b + c)² - (a² + b² + c²)}}{2} = \frac{{15 - 83}}{2} = \frac{{225 - 83}}{2}\) = 71