Question

a + b + C = 12 ab + bc + ac = 15 find the value of a square + b square + c square

Answer 1

Hope it helps............

Answer 2

a+b+c = 12

squaring both sides we get

(a+b+c)² = 144

let a+b = x

(x+c)² = 144

x² + c² + 2cx = 144

Now put the value of x in the above equation

(a+b)² + c² + 2c(a+b) = 144

After solving we get:

a²+b²+c² + 2ab + 2bc + 2ca = 144

a²+b²+c² = 144 - (2ab + 2bc + 2ca)........................................eq1

We know ab+bc+ca = 15

multiply above eq by 2 ,we get

2ab+2bc+2ca=30

Putting this in eq1, we get

a²+b²+c² = 114