If a,b,c are real numbers such that a² +2b = 7, b² + 4c = -7 and c² + 6a = -14 then the value of a²+b²+c² is:

PLEASE WRITE FULL SOUTION AND PLEASE USE THE SHORTEST POSSIBLE APPROACH.

your answer is 15.
Soln-

taking eqn 1-
a^2+2b=7
now adding b^2+1 on both side gives
a^2 +b^2+2b+1=7+b^2+1
it becomes
a^2+(b+1)^2=8+b^2 taking this eqn as (A)
similarly in eqn 2
b^2+4c=-7
adding c^2+4 on both side
it simplifies and becomes
b^2+(c+2)^2=-3+c^2 taking this eqn as (B)

similarly in eqn3
adding a^2+9 on both side,
it becomes
c^2+(a+3)^2=-5+a^2 taking this eqn as (C)

now adding (A)+(B)+(C)
it simplifies and become

(b+1)^2 + (c+2)^2 + (a+3)^2 = 0
since square of a number cant be negative so
a=-3, b=-2 & c=-1
so

a2+b2+c2= 9+4+1=15

Plz Approve!

(The one who answered first) , pagla nasamajh do-do bara galti kiya hai aur puchta hai plzz approve XDDDDDDDBHUT ACCHi galtiya karte ho yaara=-3 ,B=-1 ,C=-2HogaAur , 9+4+1= 14 Hota haiXDI`m smiling so hard ,hahahahahaSorry if I hurt u ,but Ur mistakes are so funny...