Another Solving Linear/ Quadratic Eqn: intersection of y = x^3 and x + y = 10

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MathsFormula

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Find the coordinates of the point of intersection of the curve y = x3 and x + y = 10

Answer = (2,8)

My attempt:

x3 = 10 - x


x + x3 = 10

x(x2 + 1) = 10

Now stuck

Also tried y = x3

y = (y - 10)3 and then expanding BUT didn't work


Please advise
 
Well, this one's a bit more difficult than the previous one, due to the fact that no matter what you do, you'll be left with a cubic equation, rather than a quadratic. Generally speaking, cubics are difficult to factor. Personally, I'd work with the x + x3 = 10 version. If we get everything over to one side and arranged in descending power order, we're left with x3 + x - 10 = 0. At this point, while you're correct that you can factor out an x from the first two terms, that's actually counterproductive in this case. Instead, try applying the Rational Root Theorem and see how far you can get.
 
MathsFormula said:
Find the coordinates of the point of intersection of the curve y = x3 and x + y = 10

My attempt:

x3 = 10 - x

x + x3 = 10
Click to expand...
get x3 + x - 10 = 0. These are easily solved for someone in prealgebra (harder for more advanced students!!!-seriously)

At your stage you need to try trial and error.

x=1: left hand side is -8

x=2: left hand side is 0. So 2 is a solution!
 
Jomo said:
get x3 + x - 10 = 0. These are easily solved for someone in prealgebra (harder for more advanced students!!!-seriously)

At your stage you need to try trial and error.

x=1: left hand side is -8

x=2: left hand side is 0. So 2 is a solution!
Click to expand...

Thanks. Now it seems so simple BUT I would never have thought to just try guessing. How am to know when to start guessing. Maybe aa a last resort?
 
MathsFormula said:
How am to know when to start guessing.
Click to expand...

A lot of introductory exercises are cooked up to have integer answers near zero. You don't have to wait, to guess-and-check a few. You can try that, anytime. (There are other methods, too.)

Since your exercise is about the intersection of two graphs, you could also have looked at the graph and seen x=2 at the intersection point.

For example, go to google.com, and enter this: plot x^3,10-x :)
 
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