Question

If a, b, c are real no.s such that a^2+2b=6, b^2+4c= -7 and c^2+6a= -13 then value of a^2+b^2+c^2 is equal to

Answer 1

a² + 2b = 6 ------(1)
b² +4c = -7--------(2)
c² + 6a = -13 ----(3)

add all equations

a² + b² + c² +2b +4c +6a = -14

a² + 6a + 9 + b² + 2b +1 + c² + 4b +4 =0

( a +3)² + ( b+1)² + ( c +2)² = 0

so,
a + 3 = 0 then a = -3
b + 1 =0 then b = -1
c + 2 = 0 then , c = -2

now,

a² + b² + c² = (-3)² + (-1)² + (-2)² = 14