Her sien 1.3 Los op vir $$ x $$ 1.3 .1 x $$ (x-4)=- $$ 1.3 .2 5x+8

Question

Her sien 1.3 Los op vir $$ x $$ 1.3 .1 x $$ (x-4)=- $$ 1.3 .2 5x+8<3x 1.4 Los gelyktydig $$ z^{2+y} $$

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$z$$:
  $$z^{2+y}=0$$
- step1: Calculate:
  $$z=0^{\frac{1}{2+y}}$$
- step2: Simplify:
  $$z=0$$
- step3: Check if the solution is in the defined range:
  $$z=0,z>0$$
- step4: Find the intersection:
  $$z \in \varnothing $$
Solve the equation $$ 5x+8<3x $$.
Solve the inequality by following steps:
- step0: Solve for $$x$$:
  $$5x+8<3x$$
- step1: Move the variable to the left side:
  $$5x+8-3x<0$$
- step2: Subtract the terms:
  $$2x+8<0$$
- step3: Move the constant to the right side:
  $$2x<0-8$$
- step4: Remove 0:
  $$2x<-8$$
- step5: Divide both sides:
  $$\frac{2x}{2}<\frac{-8}{2}$$
- step6: Divide the numbers:
  $$x<-4$$
Solve the equation $$ x(x-4)=-1 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$x\left(x-4\right)=-1$$
- step1: Expand the expression:
  $$x^{2}-4x=-1$$
- step2: Move the expression to the left side:
  $$x^{2}-4x+1=0$$
- step3: Solve using the quadratic formula:
  $$x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4}}{2}$$
- step4: Simplify the expression:
  $$x=\frac{4\pm \sqrt{12}}{2}$$
- step5: Simplify the expression:
  $$x=\frac{4\pm 2\sqrt{3}}{2}$$
- step6: Separate into possible cases:
  $$\begin{align}&x=\frac{4+2\sqrt{3}}{2}\&x=\frac{4-2\sqrt{3}}{2}\end{align}$$
- step7: Simplify the expression:
  $$\begin{align}&x=2+\sqrt{3}\&x=\frac{4-2\sqrt{3}}{2}\end{align}$$
- step8: Simplify the expression:
  $$\begin{align}&x=2+\sqrt{3}\&x=2-\sqrt{3}\end{align}$$
- step9: Rewrite:
  $$x_{1}=2-\sqrt{3},x_{2}=2+\sqrt{3}$$
Here are the solutions to the problems you provided:

### 1.3.1 Solve for $$ x $$ in the equation $$ x(x-4) = -1 $$

To solve the equation $$ x(x-4) = -1 $$, we can rearrange it to:

$$
x^2 - 4x + 1 = 0
$$

Using the quadratic formula, we find the solutions:

$$
x_{1} = 2 - \sqrt{3}, \quad x_{2} = 2 + \sqrt{3}
$$

### 1.3.2 Solve the inequality $$ 5x + 8 < 3x $$

Rearranging the inequality gives:

$$
5x - 3x < -8
$$

This simplifies to:

$$
2x < -8
$$

Dividing both sides by 2, we find:

$$
x < -4
$$

### 1.4 Solve the equation $$ z^{2+y} = 0 $$

The equation $$ z^{2+y} = 0 $$ has no real solutions because a power of a real number is zero only when the base itself is zero. Therefore, we conclude:

$$
z \in \varnothing
$$

### Summary of Results:
- For $$ x(x-4) = -1 $$: $$ x_{1} = 2 - \sqrt{3}, \quad x_{2} = 2 + \sqrt{3} $$
- For $$ 5x + 8 < 3x $$: $$ x < -4 $$
- For $$ z^{2+y} = 0 $$: No real solutions ($$ z \in \varnothing $$)
Here are the solutions: 1. **1.3.1** Solve $$ x(x - 4) = -1 $$: $$ x = 2 - \sqrt{3} $$ or $$ x = 2 + \sqrt{3} $$ 2. **1.3.2** Solve $$ 5x + 8 < 3x $$: $$ x < -4 $$ 3. **1.4** Solve $$ z^{2+y} = 0 $$: No real solutions

Her sien 1.3 Los op vir \( x \) 1.3 .1 x \( (x-4)=- \) 1.3 .2 5x+8<3x 1.4 Los gelyktydig \( z^{2+y} \)

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