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
Molodets [167]
3 years ago
6

Find all solutions to

Mathematics
1 answer:
BARSIC [14]3 years ago
7 0

Answer:

x= 0 , \frac{1}{14} , \frac{-1}{12}

Step-by-step explanation:

Given, equation is \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x}. →→→ (1)

Now, by cubing the equation on both sides, we get

( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³

⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}×\sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64 x.

⇒ 28x + 3×\sqrt[3]{15x-1}×\sqrt[3]{13x+1} (4\sqrt[3]{x}) = 64x.        

(since from (1),  \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x})

⇒ 12× \sqrt[3]{15x-1}×\sqrt[3]{13x+1} (\sqrt[3]{x})= 36x.

⇒ 3x = \sqrt[3]{(15x-1)(13+1)(x)}.

Now, once again cubing on both sides, we get

(3x)³ = (\sqrt[3]{(15x-1)(13+1)(x)})³.

⇒ 27x³ = (15x-1)(13x+1)(x).

⇒ 27x³ = 195x³ + 2x² - x

⇒ 168x³ + 2x² - x = 0

⇒ x(168x² + 2x -1) = 0

⇒ by, solving the equation we get ,

x = 0 ; x = \frac{1}{14} ; x = \frac{-1}{12}

therefore, solution is x= 0 , \frac{1}{14} , \frac{-1}{12}

You might be interested in
Sam owes 5 dollars to x friends and $3 to her sister. She owes $23 altogether.
sergey [27]

Answer:

Sam owes 4 friends $5

Step-by-step explanation:

We can set up the equation

23 = 5x + 3

Subtract the 3 from both sides

20 = 5x

x = 4 friends

7 0
3 years ago
Two student share 3 granola bars equally. How many granola bars does eachstudent get?
Murrr4er [49]
1 and they split the other in half 
7 0
3 years ago
Read 2 more answers
A worker's wage (w) is directly proportional to the number of hours (h) worked. If $71.25 is earned for working 5 h, how much is
marissa [1.9K]

Answer:

The amount earned is $327.75

Step-by-step explanation:

If the workwr working for 5h gets $71.25, then his working for 1 hour could be said to be x.

5h = $71.25

1h = x; cross multiplying would result in

x= \frac{($71.25*1)}{5h}

x= $14.25 which is the pay for 1h

Therefore for 23 h the worker would earn

23* 14.25 = $327.75

5 0
3 years ago
What is the sum of 8 and a number?
miskamm [114]
" the sum " means add

the sum of 8 and a number...

8 + n <== ur expression
5 0
3 years ago
Read 2 more answers
The height of a right square pyramid is multiplied by 10, but the area of the base is unchanged. By what factor is the volume of
pshichka [43]

Answer:

  b 10¹

Step-by-step explanation:

Consider the volume formula:

  V = 1/3Bh . . . . B is the base area and h is the height

Replacing h by 10h gives ...

  V' = 1/3B(10h) = 10(1/3Bh) = 10V

The volume is multiplied by 10 = 10¹.

5 0
2 years ago
Other questions:
  • What is a corresponding angle?
    12·1 answer
  • I need help figuring out when to use law of sine or law of cosine?
    9·1 answer
  • Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact
    10·1 answer
  • What are the zeros of the function represented by the quadratic expression 2x^2-5x-3
    12·1 answer
  • NEED HELP ASAP
    11·1 answer
  • If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
    8·1 answer
  • Bubba weighs over 60 pounds. Write an inequality Plz help
    11·2 answers
  • HELPSKANDNEKSJJF nakajf
    5·1 answer
  • ( 3 1/8 + 4.5) division 5​
    5·2 answers
  • Put these numbers in order from least to greatest 1/8, -0.333, -1/7
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!