SOLUTION: Find all solutions of the system of equations: x^4 - y^3 = 17 3x^4 + 5y^3 = 53 I'm getting weird radical answers that just can't be right. Thank you so much!

Algebra ->  Systems-of-equations -> SOLUTION: Find all solutions of the system of equations: x^4 - y^3 = 17 3x^4 + 5y^3 = 53 I'm getting weird radical answers that just can't be right. Thank you so much!      Log On


   

Question 48266This question is from textbook College Algebra
: Find all solutions of the system of equations:
x^4 - y^3 = 17
3x^4 + 5y^3 = 53
I'm getting weird radical answers that just can't be right.
Thank you so much! This question is from textbook College Algebra

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x^4 - y^3 = 17 can be expressed as: x^4 = y^3 + 17
Plug: 3x^4 + 5y^3 = 53
3(y^3 + 17) + 5y^3 = 53
3y^3 + 51 + 5y^3 = 53
8y^3 = 2
y^3 = 1/4
y = 4^(2/3)/4
Plug:
x^4 - y^3 = 17
x^4 - (4^(2/3)/4)^3 = 17
x^4 - 1/4 = 68/4
x^4 = 67/4
x = +- 67^(1/4)4^(3/4)/4
P(67^(1/4)4^(3/4)/4,4^(2/3)/4) and P(-67^(1/4)4^(3/4)/4,4^(2/3)/4)