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
Christopher has a part-time job that pays $2,900 for the year. During the year 24% is taken out for Federal Taxes. At the end of
Assoli18 [71]

Answer:

$164 refund

Step-by-step explanation:

2900 x .24= $686 withheld

2900 x .18= $522 actually owed

686-522= $164

4 0
2 years ago
Any girls wana hand out their snaps
Nadya [2.5K]

Answer:

nah I'll pass, I just need the points :)

7 0
2 years ago
Read 2 more answers
Which of the following points are in the fourth quadrant of the xy-plane? Check all that apply.
Margaret [11]

Answer:

B and F

Step-by-step explanation:

The fourth quadrant contains a positive number for the x axis and a negative number for the y axis. (B=4,-5 and F=4,-7)

8 0
2 years ago
Quadrilateral FGHI is dilated with respect to the origin by a scale factor of 1/3 . What are the coordinates of G’?
qaws [65]
G(9,-3) being dilated by a scale factor of 1/3 is G'(3,-1) so D. All I did was divide the coordinates by 3 and there you go.
3 0
2 years ago
If a =3x^2+5x-6 and b =-2x^2 -6x+7 then A - B equals
gizmo_the_mogwai [7]

Answer:

5x^2+11x-13

Step-by-step explanation:

a=3x^2+5x-6\\b=-2x^2-6x+7

a-b=(3x^2+5x-6)-(-2x^2-6x+7)=\\3x^2+5x-6+2x^2+6x-7=\\5x^2+11x-13

Hope this helps!

3 0
3 years ago
Other questions:
  • 1. Find the circumference radius of 14 a. Give an exact answer in terms of . (1 point) b. Use ≈ 22/7 and express your answer as
    10·1 answer
  • PLEASE HELP QUICKKKKKKKKKKK
    6·1 answer
  • In 103.4, the digit 0 is in the tens place. Its value is?
    12·1 answer
  • -what is the answer <br><br> 14u7uo(1+0.05)
    9·1 answer
  • 22 divided by 4/5 <br> please help me every time i do this it isn’t right
    14·1 answer
  • Tara looks up hotel room prices for a holiday.
    8·1 answer
  • HELP OUT PLEASE!!!!
    13·1 answer
  • Write the expression as a trinomial (5c+2)(2c-1)
    8·2 answers
  • Christine sleep form 11pm until 9am what fraction of a day does Christine sleep​
    10·1 answer
  • Choose all of the terms that best describe each of the sets of lines or points.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!