Question

If a+b+c=9 and ab+bc+ac=26,finda^2+b^2+c^2

Answer 1

ab + bc + ca = 26 -----(1)

a + b + c = 9

On squaring both sides, we get

( a + b +c)^2 = 9^2

=> a^2 + b^2 + c^2 + 2ab + 2bc +2ca = 81

=> a^2 + b^2 + c^2 + 2 ( ab + bc + ca) = 81

=> a^2 + b^2 + c^2 + 2 ( 26) = 81

=> a^2 + b^2 + c^2 + 52 = 81

=> a^2 + b^2 + c^2 = 29