Question

If a + b + c = 15 and ab + bc + ca = 30, find a 2 + b 2 + c 2 .

Answer 1

Answer:

(a+b+c)²=a²+b²+c²+2ab+2bc+2ac

= (15)²=a²+b²+c²+2(ab+bc+ac)

= 225=a²+b²+c²+2(30)

= 225=a²+b²+c²+60

= 225-60=a²+b²+c²

= 165=a²+b²+c²

Answer 2

EXPLANATION.

=> a + b + c = 15

=> ab + bc + ca = 30

To find a² + b² + c².

according to the question,

As we know that,

Formula of ( a + b + c)²

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

+ ca)

put the value in above equation

we get,

=> ( 15 )² = a² + b² + c² + 2 ( 30 )

=> 225 = a² + b² + c² + 60

=> 225 - 60 = a² + b² + c²

=> a² + b² + c² = 165

Therefore,

value of ( a² + b² + c² ) = 165