IDNLearn.com: Your go-to resource for finding expert answers. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.
Sagot :
To solve the equation \(\sqrt{3x + 4} = \sqrt{3x} + 4\), you need to proceed with the following detailed steps:
1. Square both sides of the equation:
[tex]\[ \left(\sqrt{3x + 4}\right)^2 = \left(\sqrt{3x} + 4\right)^2 \][/tex]
This results in:
[tex]\[ 3x + 4 = 3x + 8\sqrt{3x} + 16 \][/tex]
2. Simplify the equation:
Subtract \(3x\) from both sides:
[tex]\[ 4 = 8\sqrt{3x} + 16 \][/tex]
3. Isolate the square root term:
Subtract 16 from both sides:
[tex]\[ -12 = 8\sqrt{3x} \][/tex]
4. Solve for \(\sqrt{3x}\):
Divide both sides by 8:
[tex]\[ -1.5 = \sqrt{3x} \][/tex]
5. Square both sides again:
[tex]\[ (-1.5)^2 = (\sqrt{3x})^2 \][/tex]
This results in:
[tex]\[ 2.25 = 3x \][/tex]
6. Solve for \(x\):
Divide by 3:
[tex]\[ x = 0.75 \][/tex]
Based on this detailed procedure, the correct statement is:
Square both sides twice and then solve the resulting linear equation.
1. Square both sides of the equation:
[tex]\[ \left(\sqrt{3x + 4}\right)^2 = \left(\sqrt{3x} + 4\right)^2 \][/tex]
This results in:
[tex]\[ 3x + 4 = 3x + 8\sqrt{3x} + 16 \][/tex]
2. Simplify the equation:
Subtract \(3x\) from both sides:
[tex]\[ 4 = 8\sqrt{3x} + 16 \][/tex]
3. Isolate the square root term:
Subtract 16 from both sides:
[tex]\[ -12 = 8\sqrt{3x} \][/tex]
4. Solve for \(\sqrt{3x}\):
Divide both sides by 8:
[tex]\[ -1.5 = \sqrt{3x} \][/tex]
5. Square both sides again:
[tex]\[ (-1.5)^2 = (\sqrt{3x})^2 \][/tex]
This results in:
[tex]\[ 2.25 = 3x \][/tex]
6. Solve for \(x\):
Divide by 3:
[tex]\[ x = 0.75 \][/tex]
Based on this detailed procedure, the correct statement is:
Square both sides twice and then solve the resulting linear equation.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.