Question:

Help From the Calculus Peoples?

by  |  earlier

0 LIKES UnLike

Solve for:

a^(2/3) - 9a^(1/3) = -20

I've asked every person I know, yahoo answers and wikipedia. Please help.

 Tags:

   Report

5 ANSWERS


  1. a^(2/3) - 9a^(1/3) = -20

    Let x = a^(1/3)

    x² = a^(2/3)

    x² - 9x = -20

    x² - 9x + 20 = 0

    (x-5)(x-4) = 0

    x = {4,5}

    a = x³

    a

    = 5³ = 125

    OR

    4³ = 64

    a = {64, 125}

    No calculus required!


  2. x= 63.99999968        

    You cannot solve this algebraically. Using Newton's method and graphing, the above solution was obtained.

  3. Seems like an algebra question to me. Completing the square or the quadratic formula will solve this.

    a^(2/3)-9a^(1/3)+20=0

    a^(1/3)=(9±√((-9)²-4*1*20)))/(2*1)

    a^(1/3)=(9±√1)/2

    a^(1/3)=(9+1)/2

    a^(1/3)=10/2=5

    a=5³=125

    a^(1/3)=(9-1)/2

    a^(1/3)=8/2=4

    a=4³=64

    So a=64 or a=125

  4. a^(2/3) - 9a^(1/3) = -20

    ( a^(2/3) - 9a^(1/3) = -20 )^3

    a^2 - 9a + 8000 = 0

    *use quadratic formula*

    a = 93.8295i , -84.8295i

    *i = sqrt(-1)  

  5. a^(2/3) = (a^(1/3))^2

    Therefore,

    a^(2/3) - 9a^(1/3) = -20

    goes to

    (a^(1/3))^2 - 9a^(1/3) + 20 = 0, after adding 20 to each side.

    Now lets factor this left side so that we can use the zero product property to solve the equation.

    (a^(1/3) - 5)(a^(1/3) - 4) = 0

    Now we see that:

    a^(1/3) - 5 = 0

    (a^(1/3) - 5)

    a = 5^3 = 125, after cubing both sides of the equation

    or

    a^(1/3) - 4 = 0

    a^(1/3) = 4

    a = 4^3 = 64, after cubing both sides.

    Therefore, we have come up with the solution that a = 125 or 64.

Question Stats

Latest activity: earlier.
This question has 5 answers.

BECOME A GUIDE

Share your knowledge and help people by answering questions.
Unanswered Questions