Question

If a2 + b2 +2c2 – 4a + 2c-2bc + 5 = 0 then the possible
value of a +b-c fAndhra Pradesh 2014-15]
(1) 1
(2)2
(3)-1
(4) 2​

Answer 1

a²+b²+2c²-4a +2c-2bc +5 =0

(a²-4a+5)+(b²-2bc+c²)+2c²+2c+5-4-c²=0

(a²-4a+5)+(b²-2bc+c²)(c²+2c+1)=0

(a-2)²+(b-c)²+(c+1)²= 0

Since each term is a square and nonnegative.

Therefore a+b+c=0

a-2= 0

a= 2

b-c=0

b=c

c+1=0

c=-1

so a=2, b = c=-1

so , a+b-c = 2-1+1=2