you could try graphing.
change to 3√x = x+6
then split it into
y = 3√x and y = x+6
a few points on the graph would be (0,0), (1,3), (4,6) and (9,9)
the second is of course a straight line with slope of 1 and y-intercept of 6
it is immediately obvious that the two graphs cannot intersect, so your equation has no real solution.
The only other option is to square both sides of 3√x = x+6 ,
to obtain the quadratic equation x^2 + 3x + 36 = 0
which only has complex roots as shown by our graph above.
I am not sure if this helps.
If we rearrange and square each side we end up with
and by inspection we see that one solution is x=3
to find the other divide
8x^2-12x-36 by x-3
8x-12=0 as the other solution
but check my maths!!
if you want a "proof" and development of the quadratic equation, it is obtained by completing the square on
Ax + By + C = 0 as shown in
(BTW, I notice that DrRuss has a small error in his solution.
when you square 3√x you get 9x not 9x^2)
OOOPS That what comes of solving things quickly!!
algebra - factor 3a^2(a-b)-6a(a-b)+21(a-b) Can you show me the steps? I'm just ...
For Hellpp - Algebra 2 - I removed your original post because of an ...
Math-Algebra - Solve: 3x-2y=10 2x+3y=-2 Graph: Substitution: Elimination: Show ...
Algebra 1 - Lately I just have blacked out in my algebra 1 class. Here's a ...
Beginning Algebra - how do i figure out this problem i have to make the equation...
Algebra - Solve: 3x-2y=10 2x+3y=-2 Graph: Substitution: Elimination: Show Your ...
math - in = x out = 2 x so if -1 is in what is out , if 0 in what out, and if 3 ...
Algebra - I can't figure out this problem... 2x-2-(x-1) = 4-1+x-(-3x) solve for ...
algebra - this is probablt really simple, but for some reason I can't find out ...
College Algebra - solve systems of equations by graphing... I get how to graph ...