Solve each equation separately and find which x is the largest.$ (\sqrt{x}+4)(\sqrt{x}-4)=0 $$ \sqrt{x}=4 $

There is no solution to the two equations

Square Root Equations: Solve (√x+4)(√x-4)=0 and √x=4 for Largest X

Q: Why does $ (\sqrt{x}+4)(\sqrt{x}-4)=0 $ give the same answer as $ \sqrt{x}=4 $ ?

The first equation uses the zero product property. Since $ \sqrt{x}+4 $ is always positive (square roots can't be negative), only $ \sqrt{x}-4=0 $ can equal zero, giving $ \sqrt{x}=4 $!

Q: What if I got x = -16 as a solution?

That's impossible! Remember that $ \sqrt{x} $ requires x ≥ 0. Negative values under the square root don't give real solutions. Always check your domain!

Q: How do I solve the zero product form?

Set each factor equal to zero: $ \sqrt{x}+4=0 $ or $ \sqrt{x}-4=0 $. The first gives $ \sqrt{x}=-4 $ (impossible), so only $ \sqrt{x}=4 $ works.

Q: Why is the answer "2 = 1" instead of just x = 16?

The question asks to compare which x is largest between the two equations. Since both equations give x = 16, they're equal! The answer "2 = 1" means equation 2 equals equation 1 in terms of their solutions.

Q: Can I use the difference of squares formula here?

Yes! $ (\sqrt{x}+4)(\sqrt{x}-4) $ equals $ (\sqrt{x})^2 - 4^2 = x - 16 $. Setting this equal to zero gives x = 16 directly.

Square Root Equations with Product Form

Solve each equation separately and find which x is the largest.

$(\sqrt{x}+4)(\sqrt{x}-4)=0$
$\sqrt{x}=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:14 Let's find the largest value of X.

00:18 First, we'll determine X from section one.

00:27 Let's use the multiplication formulas to simplify the expression.

00:48 Remember, the square root squared is just the number.

00:52 Now, calculate four squared.

00:56 Isolate X to find its value.

01:00 This is the value of X from section one.

01:07 Next, let's find X from section two.

01:11 Square the expression to remove the root.

01:21 Here's X from section two.

01:25 We see that the X values are equal in both sections.

01:30 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve each equation separately and find which x is the largest.

$(\sqrt{x}+4)(\sqrt{x}-4)=0$
$\sqrt{x}=4$

Step-by-step solution

To solve these equations, we'll follow these steps:

Step 1: Solve $(\sqrt{x}+4)(\sqrt{x}-4)=0$
Step 2: Solve $\sqrt{x}=4$
Step 3: Compare both solutions to find the largest value of $x$

Let's work through each step:

Step 1: For the equation $(\sqrt{x}+4)(\sqrt{x}-4)=0$ , note that it is in the form of a difference of squares: $a^2 - b^2 = (a-b)(a+b) = 0$ . Here, $a = \sqrt{x}$ and $b = 4$ , giving:

a^2 - b^2 = (\sqrt{x})^2 - 4^2 = x - 16 = 0

This simplifies to $x - 16 = 0$ , meaning $x = 16$ .

Step 2: For the equation $\sqrt{x} = 4$ , squaring both sides yields:

(\sqrt{x})^2 = 4^2

x = 16

Step 3: Now that both equations result in $x = 16$ , there is only one unique solution. Comparing the single value from each equation, $x = 16$ is the largest.

Therefore, the largest $x$ is $x = 16$ .

Final Answer

2=1

Key Points to Remember

Essential concepts to master this topic

Domain Rule: Square root requires x ≥ 0 for real solutions
Zero Product: If (a)(b) = 0, then a = 0 or b = 0
Check: Substitute x = 16: $\sqrt{16} = 4$ in both equations ✓

Common Mistakes

Avoid these frequent errors

Ignoring domain restrictions
Don't solve algebraically without checking x ≥ 0 first = negative solutions that don't work! Square roots are only defined for non-negative numbers in real solutions. Always verify your answer satisfies the domain restriction.

Practice Quiz

Test your knowledge with interactive questions

Solve:

$$ (2+x)(2-x)=0 $$

FAQ

Everything you need to know about this question

Why does $(\sqrt{x}+4)(\sqrt{x}-4)=0$ give the same answer as $\sqrt{x}=4$ ?

The first equation uses the zero product property. Since $\sqrt{x}+4$ is always positive (square roots can't be negative), only $\sqrt{x}-4=0$ can equal zero, giving $\sqrt{x}=4$ !

What if I got x = -16 as a solution?

That's impossible! Remember that $\sqrt{x}$ requires x ≥ 0. Negative values under the square root don't give real solutions. Always check your domain!

How do I solve the zero product form?

Set each factor equal to zero: $\sqrt{x}+4=0$ or $\sqrt{x}-4=0$ . The first gives $\sqrt{x}=-4$ (impossible), so only $\sqrt{x}=4$ works.

Why is the answer "2 = 1" instead of just x = 16?

The question asks to compare which x is largest between the two equations. Since both equations give x = 16, they're equal! The answer "2 = 1" means equation 2 equals equation 1 in terms of their solutions.

Can I use the difference of squares formula here?

Yes! $(\sqrt{x}+4)(\sqrt{x}-4)$ equals $(\sqrt{x})^2 - 4^2 = x - 16$ . Setting this equal to zero gives x = 16 directly.

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Square Root Equations: Solve (√x+4)(√x-4)=0 and √x=4 for Largest X

Square Root Equations with Product Form

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does $(\sqrt{x}+4)(\sqrt{x}-4)=0$ give the same answer as $\sqrt{x}=4$ ?

What if I got x = -16 as a solution?

How do I solve the zero product form?

Why is the answer "2 = 1" instead of just x = 16?

Can I use the difference of squares formula here?

🌟 Unlock Your Math Potential

More Questions

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Solve the Quadratic Equation: (√x + 1/2)(√x - 1/2) = 0

Resolve the Quadratic Equation: x² + 2x - 24 = -13 + (x-6)(x+6) + 7x

Square Root Equations: Solve (√x+4)(√x-4)=0 and √x=4 for Largest X

Square Root Equations with Product Form

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does (x+4)(x−4)=0 (\sqrt{x}+4)(\sqrt{x}-4)=0 (x​+4)(x​−4)=0 give the same answer as x=4 \sqrt{x}=4 x​=4?

What if I got x = -16 as a solution?

How do I solve the zero product form?

Why is the answer "2 = 1" instead of just x = 16?

Can I use the difference of squares formula here?

🌟 Unlock Your Math Potential

More Questions

Difference of squares

Solve and Compare: Tackle the Equations 3 + x + 17 - 56x = 18x + 44 and (x-2)(x+2) = 0

Solve and Compare: Delving into (√x+8)(√x-8)=0 and x²-100=0

Solve the Quadratic Equation: (√x + 1/2)(√x - 1/2) = 0

Resolve the Quadratic Equation: x² + 2x - 24 = -13 + (x-6)(x+6) + 7x

Why does $(\sqrt{x}+4)(\sqrt{x}-4)=0$ give the same answer as $\sqrt{x}=4$ ?