can you show me the steps how to do this?
square root of 3-x + square root of 3+x = x
sqrt(3-x) + sqrt (3+x) = x
(sqrt(3-x) + sqrt (3+x))^2 = x^2 but check at the end because -something ^2 is the same as something^2
(3-x) +2 sqrt(3-x)sqrt(3+x) +(3+x) = x^2
6 + 2 sqrt[(3-x)(3+x)] = x^2
6 + 2 sqrt[ 9 -x^2] = x^2
2 sqrt [ 9-x^2] = x^2-6
4 (9-x^2) = x^4 - 12 x^2 + 36
36 -4 x^2 = x^4 -12 x^2 + 36
x^4 - 8 x^2 = 0
x^2 (x^2-8) = 0
x = 0 or 0 or 2 sqrt 2 or -2 sqrt 2
try 0, no
2 sqrt 2 = 2.82 = yes
-2sqrt 2 = -2.82 yes
those both work but 0 does not
Square both sides. Then bring all terms except the remaining square root to one side and then square again. Put x^2 = t in that equation and solve the quadratic equation in t.
Sure! To solve the given equation "square root of (3-x) + square root of (3+x) = x," you can follow these steps:
Step 1: Isolate one of the square root terms on one side of the equation.
Start by moving one of the square root terms to the other side of the equation. Let's move the square root of (3+x) to the right side:
square root of (3-x) = x - square root of (3+x)
Step 2: Square both sides of the equation to eliminate the square root.
By squaring both sides of the equation, you remove the square root symbol. Be aware that squaring both sides might introduce extraneous solutions, so you will need to check your answers later.
(square root of (3-x))^2 = (x - square root of (3+x))^2
3 - x = x^2 - 2x(square root of (3+x)) + (3 + x)
Simplifying this equation further:
3 - x = x^2 + 2x - 2x(square root of (3+x))
Step 3: Collect like terms.
Rearrange the equation to have all the variables on one side and constant terms on the other side:
x^2 + (2x - 2x(square root of (3+x))) - x - 3 = 0
Combine like terms:
x^2 + (x - 2x) - 2x(square root of (3+x)) - 3 = 0
Simplify further:
x^2 - x - 2x(square root of (3+x)) - 3 = 0
Step 4: Solve the equation.
To solve this quadratic equation, you can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± (square root of (b^2 - 4ac)))/(2a)
In our equation, the coefficients are:
a = 1, b = -1, c = (-2(square root of (3+x)) - 3)
Substitute these values into the quadratic formula:
x = (1 ± (square root of (1 - 4(1)(-2(square root of (3+x)) - 3)))) / 2(1)
Simplify further if possible and solve for x.
Please note that solving this equation analytically might not lead to a simple exact value for x, and there might be multiple solutions or no real solutions at all.