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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.)

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8 0
2 years ago
Answer in standard form PLEASE.
matrenka [14]

0.9 x 10^4

Let’s break this down into steps.

So to start off with, you need to do 4.5/5 which = 0.9.

Now we can deal with the indices. 10^-3 / 10^-7 means we have to subtract them. Therefore, -3 - -7 = 4. Altogether, we have 0.9 x 10^4

The question states we should leave our answer in standard form.

So our answer is 0.9 x 10^4.
8 0
2 years ago
X^2-3=5x simplify this
Alex Ar [27]
To simplify x^2-3 =5x

You would first subtract 5x from both sides

X^3-5x-3

Next you would plug this into the quadratic equation:

X=5+/- the square root of: -5^2 -4(1)(-3)/2(1)

Then simplify,
5+/- the squareroot of 24 + 12 / 2

5+/- The squareroot of 36 /2

5+/- 6 / 2

Then solve if it’s an addition or subtract

5+6/2

X=11/2 or 5 1/2

5-6/2

X= -1/2

The answer is x=-1/2 or x=11/2

Hope this helps

7 0
3 years ago
A box of cereal contains 6 cups of cereal each serving is 1/3 of a cup how many servings are in the box
Thepotemich [5.8K]
6 ÷ 1/3 = 6/1 x3/1 = 18 servings per box
6 0
3 years ago
Apply the distributive property to factor out the greatest common factors 9 +15
aleksley [76]

Answer:

3( 3+5)

Step-by-step explanation:

9 +15

Rewriting 9 as 3*3  and 15 * 3*5

3*3 + 3*5

Factor out 3

3( 3+5)

3 0
2 years ago
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