Math / Algebra

QuestionWhich equation can be rewritten as $x+4=x^{2}$ ? Assume $x>0$
$\sqrt{x}+2=x$
$\sqrt{x+2}=x$ $\sqrt{x+4}=x$ $\sqrt{x^{2}+16}=x$

Studdy Solution

STEP 1

1. We are given four equations and need to determine which one can be rewritten as $x + 4 = x^2$ .
2. We assume $x > 0$ for all equations.
3. We need to manipulate each equation to see if it can be transformed into $x + 4 = x^2$ .

STEP 2

1. Analyze each equation individually.
2. Transform each equation to see if it matches $x + 4 = x^2$ .
3. Identify the correct equation.

STEP 3

Analyze the first equation: $\sqrt{x} + 2 = x$ .
Subtract 2 from both sides:
$\sqrt{x} = x - 2$
Square both sides to eliminate the square root:
$x = (x - 2)^2$
Expand the right side:
$x = x^2 - 4x + 4$
Rearrange to compare with $x + 4 = x^2$ :
$x^2 - 5x + 4 = 0$
This does not match $x + 4 = x^2$ .

STEP 4

Analyze the second equation: $\sqrt{x+2} = x$ .
Square both sides to eliminate the square root:
$x + 2 = x^2$
This matches the form $x + 4 = x^2$ if we adjust the constant term.

STEP 5

Analyze the third equation: $\sqrt{x+4} = x$ .
Square both sides to eliminate the square root:
$x + 4 = x^2$
This matches the form $x + 4 = x^2$ exactly.

STEP 6

Analyze the fourth equation: $\sqrt{x^2 + 16} = x$ .
Square both sides to eliminate the square root:
$x^2 + 16 = x^2$
Subtract $x^2$ from both sides:
$16 = 0$
This is not possible, so it does not match $x + 4 = x^2$ .
The equation that can be rewritten as $x + 4 = x^2$ is $\sqrt{x+4} = x$ .

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QuestionWhich equation can be rewritten as $x+4=x^{2}$ ? Assume $x>0$
$\sqrt{x}+2=x$
$\sqrt{x+2}=x$ $\sqrt{x+4}=x$ $\sqrt{x^{2}+16}=x$

Studdy Solution

STEP 1

1. We are given four equations and need to determine which one can be rewritten as $x + 4 = x^2$ .
2. We assume $x > 0$ for all equations.
3. We need to manipulate each equation to see if it can be transformed into $x + 4 = x^2$ .

STEP 2

1. Analyze each equation individually.
2. Transform each equation to see if it matches $x + 4 = x^2$ .
3. Identify the correct equation.

STEP 3

Analyze the first equation: $\sqrt{x} + 2 = x$ .
Subtract 2 from both sides:
$\sqrt{x} = x - 2$
Square both sides to eliminate the square root:
$x = (x - 2)^2$
Expand the right side:
$x = x^2 - 4x + 4$
Rearrange to compare with $x + 4 = x^2$ :
$x^2 - 5x + 4 = 0$
This does not match $x + 4 = x^2$ .

STEP 4

Analyze the second equation: $\sqrt{x+2} = x$ .
Square both sides to eliminate the square root:
$x + 2 = x^2$
This matches the form $x + 4 = x^2$ if we adjust the constant term.

STEP 5

Analyze the third equation: $\sqrt{x+4} = x$ .
Square both sides to eliminate the square root:
$x + 4 = x^2$
This matches the form $x + 4 = x^2$ exactly.

STEP 6

Analyze the fourth equation: $\sqrt{x^2 + 16} = x$ .
Square both sides to eliminate the square root:
$x^2 + 16 = x^2$
Subtract $x^2$ from both sides:
$16 = 0$
This is not possible, so it does not match $x + 4 = x^2$ .
The equation that can be rewritten as $x + 4 = x^2$ is $\sqrt{x+4} = x$ .

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QuestionWhich equation can be rewritten as x+4=x2x+4=x^{2}x+4=x2 ? Assume x>0x>0x>0 x+2=x\sqrt{x}+2=xx​+2=xx+2=x\sqrt{x+2}=xx+2​=x x+4=x\sqrt{x+4}=xx+4​=x x2+16=x\sqrt{x^{2}+16}=xx2+16​=x

Studdy Solution

STEP 1

1. We are given four equations and need to determine which one can be rewritten as x+4=x2 x + 4 = x^2 x+4=x2.2. We assume x>0 x > 0 x>0 for all equations.3. We need to manipulate each equation to see if it can be transformed into x+4=x2 x + 4 = x^2 x+4=x2.

STEP 2

1. Analyze each equation individually.2. Transform each equation to see if it matches x+4=x2 x + 4 = x^2 x+4=x2.3. Identify the correct equation.

STEP 3

STEP 4

Analyze the second equation: x+2=x\sqrt{x+2} = xx+2​=x.Square both sides to eliminate the square root:x+2=x2 x + 2 = x^2 x+2=x2This matches the form x+4=x2 x + 4 = x^2 x+4=x2 if we adjust the constant term.

STEP 5

Analyze the third equation: x+4=x\sqrt{x+4} = xx+4​=x.Square both sides to eliminate the square root:x+4=x2 x + 4 = x^2 x+4=x2This matches the form x+4=x2 x + 4 = x^2 x+4=x2 exactly.

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhich equation can be rewritten as $x+4=x^{2}$ ? Assume $x>0$
$\sqrt{x}+2=x$
$\sqrt{x+2}=x$ $\sqrt{x+4}=x$ $\sqrt{x^{2}+16}=x$

1. We are given four equations and need to determine which one can be rewritten as $x + 4 = x^2$ .
2. We assume $x > 0$ for all equations.
3. We need to manipulate each equation to see if it can be transformed into $x + 4 = x^2$ .

1. Analyze each equation individually.
2. Transform each equation to see if it matches $x + 4 = x^2$ .
3. Identify the correct equation.

Analyze the second equation: $\sqrt{x+2} = x$ .
Square both sides to eliminate the square root:
$x + 2 = x^2$
This matches the form $x + 4 = x^2$ if we adjust the constant term.

Analyze the third equation: $\sqrt{x+4} = x$ .
Square both sides to eliminate the square root:
$x + 4 = x^2$
This matches the form $x + 4 = x^2$ exactly.