1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ksju [112]
3 years ago
14

Please,look at this one.

Mathematics
1 answer:
Ket [755]3 years ago
4 0

9514 1404 393

Answer:

  x = √2

Step-by-step explanation:

A graph indicates the only solution is near x=√2.

__

Square both sides, separate the radical and do it again.

  \displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}

Now, we can put this polynomial equation into standard form and factor it.

  x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}

The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].

The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.

The only solution is x = √2.

_____

<em>Additional comment</em>

For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)

You might be interested in
Solve the system by graphing.
nlexa [21]

When solving a system by graphing you need to see where the lines intersect.

Below is a picture of these lines graphed. The green line is y = x +4 and the blue line is y = 4x - 1

The red dot represents the intersection is about (1, 5)

The original point is: (1.667, 5.667)

Hope this helped!

4 0
3 years ago
Find the inverse f(x) = 4x+2
alexdok [17]

Answer:

Let's solve for x.

y=4x+2

Step 1: Flip the equation.

4x+2=y

Step 2: Add -2 to both sides.

4x+2+−2=y+−2

4x=y−2

Step 3: Divide both sides by 4.

4x/4=y−2/4

x=1/4y+ −1/2

Answer:

x=1/4y+ −1/2

Close Ad

Step-by-step explanation:

4 0
3 years ago
Find 3 different ratios that are equivalent 7:3 explain why these ratios are equivalent
kkurt [141]

Answer:

7:3, 14:6, 28:12

multiples.. hope that helps.

6 0
3 years ago
ABDF is a regular hexagon. What is the measure of angle A?
dolphi86 [110]

720 \div 6 = 120
4 0
3 years ago
6. Describe, step-by-step how to find the slope of a line through two points.
Margarita [4]

Answer:

Step-by-step explanation:

The slope is the difference in y-coordinates of the 2 points divided by the corresponding difference in x-coordinates.

For example:

Find the slope of the line joining the points (3, 5) and (-2, 1)

The slope = (5 - 1) / (3 - (-2))

= 4/(3+2)

= 4/5.

NOTE:

You would get the same result if you reversed the values

- that is (1 - 5)/(-2 - 3

= -4/-5

= 4/5.

The important thing to remember is to use <em>corresponding </em>values in the calculation.

5 0
3 years ago
Other questions:
  • True or False?
    6·1 answer
  • Find the solution set <br><br>2x^2 -2x -4 =0<br><br>please use a comma to separate your answer.
    9·1 answer
  • Find the value of X in the problem below. Geometry
    6·1 answer
  • What are the solutions to the equation?
    7·1 answer
  • Who do you write 0.632 into word form
    8·1 answer
  • Dave has had a gym membership for 10 weeks. He goes to the gym 5 times a week. Each visit, he exercises for 1.75 hours. He spend
    9·1 answer
  • NEED HELP NOW!!!!
    7·1 answer
  • Math question plz help
    13·1 answer
  • Absolute value of 35+|-35|=​
    13·2 answers
  • I need help with this one some one help pls
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!