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
slega [8]
3 years ago
12

Find one value of x that is a solution to the equation:(x^2– 8)^2 + x^2 – 8 = 20x=​

Mathematics
1 answer:
Kipish [7]3 years ago
8 0

Answer:

x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)

Step-by-step explanation:

Solve for x:

-8 + x^2 + (x^2 - 8)^2 = 20

Expand out terms of the left hand side:

x^4 - 15 x^2 + 56 = 20

Subtract 20 from both sides:

x^4 - 15 x^2 + 36 = 0

Substitute y = x^2:

y^2 - 15 y + 36 = 0

The left hand side factors into a product with two terms:

(y - 12) (y - 3) = 0

Split into two equations:

y - 12 = 0 or y - 3 = 0

Add 12 to both sides:

y = 12 or y - 3 = 0

Substitute back for y = x^2:

x^2 = 12 or y - 3 = 0

Take the square root of both sides:

x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0

Add 3 to both sides:

x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3

Substitute back for y = x^2:

x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3

Take the square root of both sides:

Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)

You might be interested in
Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 R (b) The f
Harlamova29_29 [7]

The summand (R?) is missing, but we can always come up with another one.

Divide the interval [0, 1] into n subintervals of equal length \dfrac{1-0}n=\dfrac1n:

[0,1]=\left[0,\dfrac1n\right]\cup\left[\dfrac1n,\dfrac2n\right]\cup\cdots\cup\left[1-\dfrac1n,1\right]

Let's consider a left-endpoint sum, so that we take values of f(\ell_i)={\ell_i}^3 where \ell_i is given by the sequence

\ell_i=\dfrac{i-1}n

with 1\le i\le n. Then the definite integral is equal to the Riemann sum

\displaystyle\int_0^1x^3\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^n\left(\frac{i-1}n\right)^3\frac{1-0}n

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=1}^n(i-1)^3

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=0}^{n-1}i^3

=\displaystyle\lim_{n\to\infty}\frac{n^2(n-1)^2}{4n^4}=\boxed{\frac14}

8 0
3 years ago
Which expression is equivalent to this one?
V125BC [204]
A. 6(k + s)
It's the distributive property. 
5 0
2 years ago
Read 2 more answers
There are 8 sophomores on the academic team. At the last competition, they each took the math test. Their scores were 82%, 92%,
castortr0y [4]

Median would be 80.75 or 79


8 0
2 years ago
Read 2 more answers
What is the slope of this line?
anygoal [31]

Answer:

35^67

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Hello can somedy help me please <br> thank you in advance
alina1380 [7]

Answer:

Area of the circle=πr²

= 3.142 \times  {4}^{2}  \\  = 50.272cm \\  = 50.3cm

4 0
2 years ago
Other questions:
  • (e) The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3.
    13·2 answers
  • What is 8/25 as a percent
    12·2 answers
  • What does x = ? <br><br> Somebody please help me
    11·1 answer
  • This is due today and im not sure how to do it :[
    9·1 answer
  • Help loll i’m confused
    10·1 answer
  • Write an equation of the line passing through the given points.<br> (3,-25) and (-3,5)<br><br> y=
    11·2 answers
  • Solve for x.<br> 1/3 (3/2x-3)=-5/6x
    8·2 answers
  • Find the equation of the line that passes through the points (3,-2) and (-1,6) Explain
    14·1 answer
  • A healthy human heart beats about 1,533,000 times in a year. A sparrow's heart beats about 241,776,000 times in a year.
    14·1 answer
  • Five double-digit numbers We have five consecutive positive double-digit integers. If we swap places on the numbers in the large
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!