sqrt(1+x) -sqrt(1-x) = sqrt (1-x-sqrt(1+x))

Please help
This question is.....
.
.
√(1+x) - √(1-x) = whole root under OR
√1-x-√(1+x)

Please help me

your original thinking that

sqrt(1+x) -sqrt(1-x) = sqrt (1-x-sqrt(1+x))
is incorrect

test it with a value of x
e.g. suppose x = .5
then you would have
√1.5 - √.5 = √(1 - .5 + √1.5 )
or
appr .5176 = appr .455 , not even close

What was the rest of the question?

But how did you get +√1.5 it's-√1.5

But still according to you the question is incomplete.
However if x=0 then you would get a true equation. But how do I solve it to get even at least 0

If you're trying to solve the equation,

√(1+x) - √(1-x) = √(1-x-√(1+x))
(√(1+x) - √(1-x)) = √(1-x-√(1+x))^2
(1+x) - 2√(1-x^2) + (1-x) = 1-x-√(1+x)
2 - 2√(1-x^2) = 1-x-√(1+x)
1+x = 2√(1-x^2)-√(1+x)
(1+x)^2 = 4(1-x^2) - 4√((1-x^2)(1+x)) + (1+x)
5x^2+x-4 = -4(x+1)√(1-x)
(5x^2+x-4)^2 = 16(x+1)(1-x)
25x^4+26x^3-23x^2-24x = 0
x(x+1)^2(25x-24) = 0

x = 1, 0, 24/25

Check for extraneous roots which might not fit the original equation.

To solve this equation, we need to isolate the square roots on one side of the equation. Let's start by moving one square root term to the right side of the equation:

√(1+x) = √(1-x) + √(1-x-√(1+x))

Now, square both sides of the equation to eliminate the square roots:

(√(1+x))^2 = (√(1-x) + √(1-x-√(1+x)))^2

Simplifying the left side:

1 + x = (√(1-x))^2 + 2√(1-x)√(1-x-√(1+x)) + (1-x-√(1+x))

Expanding the right side:

1 + x = (1-x) + 2√(1-x)√(1-x-√(1+x)) -√(1+x)

Let's simplify further:

x = 2√(1-x)√(1-x-√(1+x)) - √(1+x)

To solve for x, we need to isolate the terms containing x on one side of the equation. Let's move the x term to the left side and the other terms to the right side:

x + √(1+x) = 2√(1-x)√(1-x-√(1+x))

Now, we'll square both sides of the equation again to eliminate the remaining square roots:

(x + √(1+x))^2 = (2√(1-x)√(1-x-√(1+x)))^2

Expanding both sides:

x^2 + 2x√(1+x) + 1 + 2√(1+x)x + (1+x) = 4(1-x)(1-x-√(1+x))

Simplifying further:

x^2 + 2x√(1+x) + 1 + 2√(1+x)x + 1 + x = 4(1-x)(1-x-√(1+x))

Combining like terms:

x^2 + 4x√(1+x) + 2 + 2√(1+x)x = 4(1-x)(1-x-√(1+x))

Expanding the right side:

x^2 + 4x√(1+x) + 2 + 2√(1+x)x = 4(1 - 2x + x^2 - √(1+x) + x√(1+x))

Distributing:

x^2 + 4x√(1+x) + 2 + 2√(1+x)x = 4 - 8x + 4x^2 - 4√(1+x) + 4x√(1+x)

Now, we can simplify and cancel out similar terms:

x^2 + 4x√(1+x) + 2 + 2√(1+x)x - 4 + 8x - 4x^2 + 4√(1+x) - 4x√(1+x) = 0

Combining like terms:

-3x^2 + 16x - 2 = 0

Now, we have a quadratic equation which can be solved using factoring, completing the square, or the quadratic formula.

Alternatively, you can use online equation solvers or computer programs to find the roots of the quadratic equation.