Question - Solving an Equation with Square Roots
Solution:
The equation provided in the image is:√(x+2) + √(x−2) = 5/2To solve this equation for x, follow these steps:1. Isolate one of the square roots on one side of the equation. Let's move √(x−2) to the right side:√(x+2) = 5/2 − √(x−2)2. Now, square both sides to eliminate the square root:(√(x+2))^2 = (5/2 − √(x−2))^2x + 2 = (5/2)^2 − 2*(5/2)*√(x−2) + (√(x−2))^2x + 2 = 25/4 − 5√(x−2) + x − 23. Simplify and isolate the term involving the square root:25/4 − 4 = 5√(x−2)25 − 16 = 20√(x−2)9 = 20√(x−2)4. Divide both sides by 20 to isolate the square root:9/20 = √(x−2)5. Now, square both sides again to eliminate the square root:(9/20)^2 = (x−2)81/400 = x−26. Add 2 to both sides to solve for x:x = 81/400 + 2x = 81/400 + 800/400x = 881/400Therefore, the solution to the original equation is x = 881/400.
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