SOLUTION: Find the x-coordinates of the three points of intersection of the curve {{{y =(x)^3}}} with the line {{{y = 5x - 2}}}, expressing non-integer values in the form {{{a+-sqrtb}}}, whe

Algebra ->  Algebra  -> Coordinate-system -> SOLUTION: Find the x-coordinates of the three points of intersection of the curve {{{y =(x)^3}}} with the line {{{y = 5x - 2}}}, expressing non-integer values in the form {{{a+-sqrtb}}}, whe      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 470209: Find the x-coordinates of the three points of intersection of the curve y+=%28x%29%5E3 with the line y+=+5x+-+2, expressing non-integer values in the form a%2B-sqrtb, where a and b are integers.

*Please answer as soon as possible bro :) =)
Answer by robertb(4012) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for the x-coordinates of the three points of intersection:
x%5E3+=+5x+-+2 <==> x%5E3+-+5x+%2B+2+=+0
<==> %28x+-+2%29%28x%5E2+%2B+2x+-+1%29+=+0
Have to solve x - 2 = 0, and x%5E2+%2B+2x+-+1+=+0
The first equation has root x = 2.
The second equation has roots x = -1+%2B-+sqrt%282%29, by direct use of the quadratic formula.