If the value of (a + b - 2)2 + (b + c - 5)2 + (c + a - 5)2 = 0, then the value of √((b + c)a + (c + a)b - 1) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 3
Explanation:
(a + b - 2)2 + (b + c - 5)2 + (c + a - 5)2 = 0
LHS:
(a+b-2)2 +(b+c-5)2 +(c+a-5)2
= (0)2 +(0)2 +(0)2
= 0
= RHS
a + b - 2 = 0
a + b = 2 ---(1)
b + c - 5 = 0
b + c = 5 ---(2)
c +a - 5 = 0
a + c = 5 ---(3)
Eq(1) + (2) + (3),
2(a + b + c) = 2 + 5 + 5
a + b + c = 6
put the value from eq(1),
2 + c = 6
c = 4
From eq(2),
b + 4 = 5
b = 1
From eq(1),
a + 1 = 2
a = 1
√((b + c)a + (c + a)b - 1)
= √((5)a + (5)b - 1)
= √((5)1 + (5)1)
√9 = 3