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
Ray Of Light [21]
3 years ago
5

Find all solutions to

Mathematics
1 answer:
SVEN [57.7K]3 years ago
8 0

Answer:

Solution is x= 0 , x = \frac{1}{14}  , x = \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.

(since (a+b)³ = a³ + b³ + 3ab(a+b) ).

⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} +  \sqrt[3]{13x+1})  = 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]{15x-1}×\sqrt[3]{x}= 36x.

⇒ 3x = \sqrt[3]{(15x-1)(13x+1)(x)} .

Now, once again cubing on both sides, we get

(3x)³ = (\sqrt[3]{(15x-1)(13x+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 , x = \frac{1}{14}   ,  x = \frac{-1}{12}

You might be interested in
What’s the distance for someone that drove 60 miles for 12 hours
Colt1911 [192]

Answer:

720 miles.

Step-by-step explanation:

Going 60 miles per hour for 12 hours would amount to driving 720 miles in total.

3 0
3 years ago
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually g
mr Goodwill [35]

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

4 0
3 years ago
Read 2 more answers
3(2c-8) - 10c > 0 can some one explain how to solve this ?​
Jet001 [13]

Answer:

c < - 6

Step-by-step explanation:

Given

3(2c - 8) - 10c > 0 ← distribute and simplify left side

6c - 24 - 10c > 0

- 4c - 24 > 0 ( add 24 to both sides )

- 4c > 24

Divide both sides by - 4, reversing the inequality symbol as a consequence of dividing by a negative quantity.

c < - 6

8 0
3 years ago
Math question below!!​
nikdorinn [45]

Answer:

A

Step-by-step explanation:

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + (x -5) = 0

(x - 5)(x + 1) = 0

x - 5 = 0   ; x + 1 = 0

x = 5      ; x = -1

7 0
3 years ago
If side AB is parallel to side DC, how are side A'B' and side D'C' related? Explain.
anastassius [24]
Side A’B’ and D’C’ are related because they are both parallel which I think means that they would be the same length
7 0
2 years ago
Other questions:
  • A school holds classes from 8:00 a.m -2:00 p.m. For what percent of a 24- hour day does this school hold classes?
    15·2 answers
  • 3. What is the solu3. What is the solution of system?
    5·1 answer
  • Simplify the expression -6(10+9v)
    8·1 answer
  • How many points make a good gussian curve?
    11·1 answer
  • Can someone please send help :(
    15·1 answer
  • Please help!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you
    10·1 answer
  • Which equation is an identity?
    10·1 answer
  • Consider the function h(x) =x2 – 12x + 58.
    15·1 answer
  • Determine the period
    14·1 answer
  • How many triples of three positive integers have a product of 16?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!