college algebra

posted by .

Solve, what is the easiest way to solve this equation?

9x^4+4=13x^2 and
x^6-19x^3=216

Thanks, in advance..

  • college algebra -

    I am solving the first one.....second one you can try yourself.

    so 9x^4+4=13x^2
    this can be written,
    x^2*(9x^2-13)=-4

    as x^2 is always +ve
    so to be -ve,
    (9x^2-13)<0

    we see that
    -(sqrt(13)/3)<x<(sqrt(13)/3)
    it comes as -1.2<x<1.2


    next we will see if there is some integer solution.
    at x=1 and x=-1
    the function has its value 0
    so x=1 and x=-1 are solution to the equation.



    next we will see if there is some maxima or minima in this func,(9x^4+4-13x^2)

    after differentiating,
    and taking it =0,
    the func. has minima at +sqrt(13/18), -sqrt(13/18)



    and at x=+1, x=-1 it has value 0,
    so the another solutions are
    x=1-2*sqrt(13/18) and x=-1+2*sqrt(13/18)

    these are 4 solutions.
    Ask me if you have any doubt.

  • college algebra -

    There are two equations there.
    In the first one, let y = x^2 and solve the quadratic.
    9y^2 -13y +4 = 0
    (y -1)(9y-4) = 0
    y = 1 or 4/9
    x = sqrt(y) = +/-1 and +/-2/3

    In the second one, let y = x^3 and again solve the quadratic.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Substitution Method-Plz help

    Use the Substitution method to solve the system of equations. x + y = -4 x - y = 2 solve for x in the second equation. x= y+2 Put that in for x in the first equation: x+y=-4 (y+2) + y = -4 solve for y. Then, x= y+2 i don't get it.How …
  2. Algebra

    Can you pleas Solve the quadric equation step by step 4x square =13x+2 4x^2 = 13x + 2 subtract 13x and 2 from both sides 4x^2 - 13x - 2 = 0 Now use the quadratic formula, since it does not factor.
  3. Algebra

    Can someone verify if my answers are correct?
  4. algebra

    1)Solve by factoring:5x^2=4-19x answer=-4,1/5 2)Which quadratic equation has roots 7 and -2/3?
  5. Algebra

    Hello all - I would like to check my work on 2 problems. Solve by factoring : x^2-13x= -12 x^2-13x+12= -12 + 12 x^2-13x+12= 0 (x-1)(x-12)= 0 x = 1 , 12 Solve using the square root property: 2x^2-35=15 2x^2-35-15=0 2x^2-50=0 2(x-5)(x+5)=0 …
  6. intermidate algebra

    Solve each equadratic equation by factoring. 6^2-13x-28 36-13x-28 -13x=-36+28 x=64/13 check this, correct if wrong
  7. college math 209

    solve the equation (x+4)^2=2x^+19x+46
  8. Math

    Factor the polynomial P(x)=x^3-2x^2-13x-10. Then solve the equation P(x)=0. This is what I got: P(x)=(x+1)(x^2-3x-10) P(x)=(x+1)(x-5)(x+2) When it says solve the equation P(x)=0 does it means solve for x?
  9. college algebra

    Solve equation |x+3|=|2-x| Not sure which way to go to solve. Thanks
  10. Math

    What is the easiest way to solve an algebraic equation?

More Similar Questions