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# show that e^x-2 = x^3 has exactly two roots watch

1. show that e^x-2 = x^3 has exactly two roots by using a graph.
2. (Original post by rakib567)
show that e^x-2 = x^3 has exactly two roots by using a graph.
What've you tried doing so far?

If you're having trouble getting started, think about:

- What graph (or graphs) you need to sketch?
- What is meant by a 'root' of an equation?

Note that the question is not asking you to calculate the roots. Just to show that they exist.
3. (Original post by Lolgarithms)
What've you tried doing so far?

If you're having trouble getting started, think about:

- What graph (or graphs) you need to sketch?
- What is meant by a 'root' of an equation?

Note that the question is not asking you to calculate the roots. Just to show that they exist.
i'm just trying to draw the graph but they do not seem to meet at 2 points
4. (Original post by rakib567)
i'm just trying to draw the graph but they do not seem to meet at 2 points
you missed lolgarithm's hint

ex - 2 = x3
ex= x3 + 2
this means sketch 2 graphs and see that these graphs meet in 2 places.

(note that the gradient of ex eventually gets steeper than that of x3)
5. (Original post by TeeEm)
you missed lolgarithm's hint

ex - 2 = x3
ex= x3 + 2
this means sketch 2 graphs and see that these graphs meet in 2 places.

(note that the gradient of ex eventually gets steeper than that of x3)
so where do they intercept?
6. (Original post by rakib567)
so where do they intercept?
they should intersect in 2 places so that shows the equation has 2 solutions (roots)

where they intersect?

I do not know and the question does not ask for this.
7. (Original post by rakib567)
so where do they intercept?
The question doesn't ask you to work out where they intersect. You know that the equation in the question has two roots if you sketch graphs of both sides of the equation and show that they cross in two places. It doesn't matter where they cross, just that they *do* cross means that there are solutions to that equation.

But, as an FYI...

If you try and solve for that using algebra, you should find that you can't do it.

If you take logs of both sides, you'll get

There's not really anywhere that you can go from there to get x on its own. That's kind of the point of the question.
8. (Original post by Lolgarithms)
The question doesn't ask you to work out where they intersect. You know that the equation in the question has two roots if you sketch graphs of both sides of the equation and show that they cross in two places. It doesn't matter where they cross, just that they *do* cross means that there are solutions to that equation.

But, as an FYI...

If you try and solve for that using algebra, you should find that you can't do it.

If you take logs of both sides, you'll get

There's not really anywhere that you can go from there to get x on its own. That's kind of the point of the question.
Thanks for the explanation but i just wanted to know where the lines meet tbh.
9. (Original post by rakib567)
Thanks for the explanation but i just wanted to know where the lines meet tbh.
http://www.wolframalpha.com/input/?i=e^x-2+%3D+x^3
10. (Original post by rakib567)
show that e^x-2 = x^3 has exactly two roots by using a graph.
But the graph of e^x and graph of x^3-2 will intersect only at one place??????
11. (Original post by Arvind54)
But the graph of e^x and graph of x^3-2 will intersect only at one place??????
if you draw the graph of x^3-e^x+2 then you will see it will cut x-axis at two places.

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