VERY DIFFICULT QUESTIONON MATH... PLEASE HELP!!?

( x-1) ^1/2 = 2- x^1/2

SQUARE BOTH SIDES

x-1 = 4 + x - 4x^1/2

4x^1/2 = 4+ x -x +1

4x^1/2 = 5

SQUARE BOTH SIDES

16x = 25

x = 25/16 ANSWER

√(x - 1) = 2 - √x

first of all the square roots must give real values

furthermore, as √(x - 1) is positive, 2 - √x must be positive as well

therefore we have the following conditions

x - 1 ≥ 0

x ≥ 0

2 - √x ≥ 0

x ≥ 1

√x ≤ 2 ---> x ≤ 4

x must be in the interval [1,4]

1 ≤ x ≤ 4

then we square both sides

(√(x - 1))² = (2 - √x)²

x - 1 = 4 - 4√x + x

move the square root in the left hand side and the other stuff in the right

4√x = 5

√x = 5/4

x = 25/16

Square the whole equation;

{(x-1)^(1/2)}^2={2-x^(1/2)}^2

= (x-1)=(4-x)

collect like terms;

x+x=4+1

2x=5

x=5/2

√(x – 1) = 2 – √x ----------- square both sides

x – 1 = 4 – 4√x + x

– 1 = 4 – 4√x

4√x = 5 ---------- square both sides

16x = 25

x = 25/16

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