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
nalin [4]
3 years ago
9

Please help solve this system of equations

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

Make a substitution:

\begin{cases}u=2x+y\\v=2x-y\end{cases}

Then the system becomes

\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}

Simplifying the equations gives

\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}

which is to say,

\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}

\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81

\implies\dfrac uv=\pm27

\implies u=\pm27v

Substituting this into the new system gives

\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1

\implies u=\pm27

Then

\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13

(meaning two solutions are (7, 13) and (-7, -13))

You might be interested in
Solve for x. X/3 = 5/8
Aleks04 [339]
The best way to solve this one would be simple cross multiplying. Multiply the top of one side with the bottom of the other side. In this problem you need to multiply X with 8 and multiply 3 with 5. You'll get an equation of 8X=15, then divide both sides by 8 so that you get X by itself. Your answer will them be X=1.875
3 0
3 years ago
there are 98 girls at Ross elementary there are 15 less boys then girls how many boys and girls are at Ross elementary​
Luba_88 [7]
Answer: 98-15= 83 boys
8 0
3 years ago
Maria sells paintings in an art gallery. She earns $375 each week plus a commission equal to 2.5% of her sales. This week her is
Dennis_Churaev [7]

Answer:

im not 100% sure but i think its 9.375

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
This is VERY URGENT, so 50 points if you answer correctly!
mariarad [96]

Answer:

The circumference is 31.43 cm

The ratio of the circumference to the diameter is equal to 3:1

Step-by-step explanation:

Thed formular for the circumference of a circle is 2\pir or \pid

where d = diameter and r = radius

if d = 10 cm, and \pi = 3.143, then circumference of the circle can be given as

3.143*10 = 31.43 cm

The ratio of the circumference to the diameter can be given as 31.43:10

and that can be given as 3.143:1

or 3:1, for the nearest whole number

3 0
3 years ago
Need help ASAP find the value of x
Brrunno [24]

Answer:

32 degrees

Step-by-step explanation:

The interior angles of a triangle always add up to 180.

Subtract the sum of 106 and 42 from 180.

180-(106+42)

180-(148)

32

x is equal to 32 degrees.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Will positive numbers always have a higher absolute value than negative numbers?
    5·1 answer
  • Then p=3.<br> Use the equation k = 3n to find the value of k when n = 3.
    6·1 answer
  • Hot dogs at a carnival cost 2.99 each plus 7%tax.what is the total cost for one hot dog?
    9·1 answer
  • What property is 6x + (7 + 2x) = 6x + (2x + 7)
    13·2 answers
  • The width of rectangular solid is 20ft, which is 4/5 of its length. The height of it is 2/9 of the sum of the length and width.
    6·1 answer
  • Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many
    6·1 answer
  • The graph of function g has x-intercepts at x = -1 and x = 3 and a y-intercept at y = -3. Select the graph that could model func
    12·1 answer
  • I need help! Question is in the picture!
    6·2 answers
  • Pls help me 10 points
    11·1 answer
  • Question below in photo!! Please answer! Will mark BRAINLIEST! ⬇⬇⬇⬇⬇⬇⬇
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!