Question #6451227Fill in the Blank
Algebra-2
Question
Solve the equation and find the value of x.
Answer & Analysis
Analysis
Question Analysis
This question involves solving a square root radical equation with two radicals. The main focus is on isolating one radical, squaring both sides to reduce the number of radicals, and repeating the process until no radicals remain—then verifying solutions.
This question involves solving a square root radical equation with two radicals. The main focus is on isolating one radical, squaring both sides to reduce the number of radicals, and repeating the process until no radicals remain—then verifying solutions.
Key Concept Explanation
Two-Radical Equations: Isolate one radical first (choose the simpler one), square to eliminate it, then simplify and isolate the remaining radical. Repeat squaring to remove the second radical.
Double Verification: Each squaring step increases extraneous root risk, so verify all solutions in the original equation.
Two-Radical Equations: Isolate one radical first (choose the simpler one), square to eliminate it, then simplify and isolate the remaining radical. Repeat squaring to remove the second radical.
Double Verification: Each squaring step increases extraneous root risk, so verify all solutions in the original equation.
Step-by-step Solution
1. Isolate one radical (e.g., ):
.
2. Square both sides to eliminate :
→ .
3. Simplify the equation to isolate the remaining radical:
1. Isolate one radical (e.g., ):
.
2. Square both sides to eliminate :
→ .
3. Simplify the equation to isolate the remaining radical:
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