If √ (2x + 2) − √x =1 ,find x.
A
x = 1 twice
B
x = 0 or 1
C
x = 3 or 1
D
x = 2 twice
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
√(2x + 2 ) − √x = 1
√(2x + 2) = 1 + √x
Square both sides
√(2x + 2)2 = (1 + √x)2
((2x + 2)2)½ = 1 + √x + √x+ x
2x + 2 = 1 + 2√x +x
Collect the like term together
2x − x + 2 − 1 = 2 √x
x + 1 = 2√x
Square both sides
(x + 1)2 = (2√x)2
x2 + 2x + 1 = 4x
x2 + 2x − 4x + 1 = 0
(x2− x)(x + 1)= 0
x(x − 1) −1(x − 1)
(x − 1)(x −1)
Either (x − 1) = 0 or (x − 1) = 0
x = 1 or 1
x = 1 twice
Source: Myschool Past Questions Archive (Record #41292)