√(x+5)-√(x-3)=2
http://www.wolframalpha.com/input/?i=%E2%88%9A%28x%2B5%29-%E2%88%9A%28x-3%29%3D2
Start by adding √(x - 3) to both sides (whatever operation you do to one side of an equation you must do to the other side as well). The result is this:
√(x + 5) = √(x - 3) + 2
Then square both sides to get this:
x + 5 = x - 3 + 2√(x - 3) + 2√(x - 3) + 4
Combine like terms:
x + 5 = x + 1 + 4√(x - 3)
Subtract x and 1 from both sides:
4 = 4√(x - 3)
Divide by 4 to get this result:
1 = √(x - 3)
Square both sides again to get this result:
1 = x - 3
x = 4
Check this solution with the original equation. It always helps to check your work!
I hope this helps.
To solve the equation √(x+5) - √(x-3) = 2, we need to isolate the variable x. Let's go step by step:
Step 1: Start by isolating one of the square roots on one side of the equation. In this case, let's isolate √(x+5). To do this, we move √(x-3) to the other side of the equation by adding it to both sides:
√(x+5) = √(x-3) + 2
Step 2: Next, square both sides of the equation to remove the square root on the left side. Squaring cancels out the square root.
(√(x+5))^2 = (√(x-3) + 2)^2
Simplifying this equation gives us:
x + 5 = (x-3) + 4√(x-3) + 4
Step 3: Now, let's simplify the right side of the equation. Combine like terms:
x + 5 = x - 3 + 4√(x-3) + 4
Simplifying further gives us:
x + 5 = x + 1 + 4√(x-3)
Step 4: Subtract x from both sides to get rid of the x term on the right side:
5 = 1 + 4√(x-3)
Step 5: Subtract 1 from both sides:
4 = 4√(x-3)
Step 6: Divide both sides by 4 to isolate the square root:
1 = √(x-3)
Step 7: Square both sides of the equation to eliminate the square root:
1^2 = (√(x-3))^2
1 = x - 3
Step 8: Add 3 to both sides to solve for x:
1 + 3 = x
x = 4
So, the solution to the equation √(x+5) - √(x-3) = 2 is x = 4.