Question - Solving a Square Root Equation
mathsolving square root equationisolate square rootseliminate square root termssimplify mathematical equations
Solution:
The mathematical expression you provided is difficult to read due to the low resolution of the image, but here is what it seems to be:√(x+7) - √(x-2) = √(x+2) - √(x-2) - (5/2)To solve for x, one would typically isolate the square roots on one side and then square both sides to eliminate the square root terms. However, there seems to be a mistake, because both sides of the equation contain the term √(x-2), which would cancel out. If this is correct, the equation after canceling the √(x-2) terms would simplify to:√(x+7) = √(x+2) - (5/2)Now let's proceed with this corrected equation.First, isolate the square root on one side:√(x+7) + (5/2) = √(x+2)Then square both sides to get rid of the square roots:(√(x+7) + 5/2)^2 = (√(x+2))^2Expand the left-hand side:(x+7) + 2*(5/2)*√(x+7) + (5/2)^2 = x + 2Simplify further by squaring (5/2) and combining like terms:x + 7 + 5√(x+7) + 25/4 = x + 2Now, isolate the square root term:5√(x+7) = x + 2 - (x + 7) - 25/45√(x+7) = -5 - 25/4Since we cannot have a square root equal to a negative number (when considering real numbers), it seems there is no solution to the equation in the real number system. Please check the original equation to ensure it has been transcribed correctly. If there is a different equation, please provide a clearer image or the correct terms.
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