solve the equation: x3-15-126=0 by cardon’s method​

Question

solve the equation: x3-15-126=0 by cardon’s method​

in progress 0
Aubrey 7 days 2021-11-22T00:16:39+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-22T00:17:50+00:00

    Given:

    An equation :-   x^{3} - 15x - 126 = 0

    To Solve:

    Solve the above equation by Cardan’s method.

    Solution:

    x^{3} - 15x - 126 = 0

    Let, x = u + v, substitute value of x in above equation,

    (u+v)^{3}-15(u+v)-126=0\\u^{3}+v^{3}  +(u+v)(3uv-15)-126=0\\

    Now, put  (3uv-15)=0

    the above equation become-

    u^{3}+v^{3}=126

    u^{3} v^{3}=74088

    Since, this equation specifies both the sum and product of u^3 and v^3 , it enables us to determine a quadratic equation whose roots are u^3 and v^3.

    Thus the equation is –

    t^{2} -15t+74088=0

    with solutions

    u^{3}=-\frac{-15}{2}  +\sqrt{\frac{-15^{2} }{4}+\frac{1}{27}  }    ;\\ v^{3}=-\frac{-15}{2}  -\sqrt{\frac{-15^{2} }{4}+\frac{1}{27}  }

     

             

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )