X^1/3 - X^1/9 = 60 find the value of x ??

2 ⤊

X^1/3 - X^1/9 = 60 find the value of x ??

2006-09-21 10:11:19 · 3 answers · asked by vinod kumar n 1 in Science & Mathematics ➔ Mathematics

3 answers

y = x^1/3
y^1/3 = x^1/9

z = y^1/3
z^3 = y

so, z^3 - z - 60 = 0

therefore
(z-4)(z^2+4z+15) = 0
(z-4) = 0 or z = 4
and
the quadratic solution is unreal (i)

Therefore the only real value of x is:
y^3 = z^9 = 262,144

2006-09-21 10:31:29 · answer #1 · answered by jimvalentinojr 6 · 0⤊ 0⤋

let x^1/9=t
t^3-t=60
t^3-t-60=0t=4 satisfies the equation
x^1/9=4
x=4^9

2006-09-21 10:20:24 · answer #2 · answered by raj 7 · 2⤊ 0⤋

using www.quickmath.com

x = 262144

2006-09-21 13:26:55 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋