Question:
If \( \sqrt{3 - 2x} = \sqrt{2x + 1} \), then \( 4x^2 = \)?
If \( \sqrt{3 - 2x} = \sqrt{2x + 1} \), then \( 4x^2 = \)?
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When solving square root equations, square both sides first to eliminate the square roots, then solve the resulting equation.
Updated On: Oct 3, 2025
- 1
- 4
- \( 2 - 2x \)
- \( 4x - 2 \)
- \( 6x - 1 \)
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The Correct Option is B
Solution and Explanation
Step 1: Square both sides of the equation.
Squaring both sides of the equation: \[ (\sqrt{3 - 2x})^2 = (\sqrt{2x + 1})^2 \implies 3 - 2x = 2x + 1 \] Step 2: Solve for \( x \).
Solving the equation for \( x \): \[ 3 - 2x = 2x + 1 \implies 3 - 1 = 2x + 2x \implies 2 = 4x \implies x = \frac{1}{2} \] Step 3: Calculate \( 4x^2 \).
Substituting \( x = \frac{1}{2} \) into \( 4x^2 \): \[ 4x^2 = 4 \times \left(\frac{1}{2}\right)^2 = 4 \times \frac{1}{4} = 1 \] \[ \boxed{4} \]
Squaring both sides of the equation: \[ (\sqrt{3 - 2x})^2 = (\sqrt{2x + 1})^2 \implies 3 - 2x = 2x + 1 \] Step 2: Solve for \( x \).
Solving the equation for \( x \): \[ 3 - 2x = 2x + 1 \implies 3 - 1 = 2x + 2x \implies 2 = 4x \implies x = \frac{1}{2} \] Step 3: Calculate \( 4x^2 \).
Substituting \( x = \frac{1}{2} \) into \( 4x^2 \): \[ 4x^2 = 4 \times \left(\frac{1}{2}\right)^2 = 4 \times \frac{1}{4} = 1 \] \[ \boxed{4} \]
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