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Sagot :
To solve the equation [tex]\(\sqrt{2x - 4} = x - 2\)[/tex], we will isolate the square root by squaring both sides of the equation. Here’s the step-by-step process:
1. Start with the given equation:
[tex]\[ \sqrt{2x - 4} = x - 2 \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{2x - 4})^2 = (x - 2)^2 \][/tex]
3. Simplify both sides after squaring:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]
Thus, the equation reduces to:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]
Keep in mind that this process may introduce extraneous solutions when squaring both sides, so any solutions found must be verified in the original equation.
1. Start with the given equation:
[tex]\[ \sqrt{2x - 4} = x - 2 \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{2x - 4})^2 = (x - 2)^2 \][/tex]
3. Simplify both sides after squaring:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]
Thus, the equation reduces to:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]
Keep in mind that this process may introduce extraneous solutions when squaring both sides, so any solutions found must be verified in the original equation.
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