C1 maths problem??? Watch

ayylmao97
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i don't understand how to answer this question:
Show that the x-coordinates of the points of intersection of
y=x(4-x) and y=x^2(7-x)
are given by the solutions to the equation x(x^2-8x+4)=0
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Smaug123
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(Original post by ayylmao97)
i don't understand how to answer this question:
Show that the x-coordinates of the points of intersection of
y=x(4-x) and y=x^2(7-x)
are given by the solutions to the equation x(x^2-8x+4)=0
Sketch out the two graphs. What can you say about where they intersect?
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Jabberjay_
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So substitute y from one of the first two equations into the other equation, expand it out, factor out x and you should be left with that last equation.
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ayylmao97
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(Original post by Smaug123)
Sketch out the two graphs. What can you say about where they intersect?
they both meet at the point (0,0)?
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ayylmao97
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(Original post by fossilcollective)
y = x (4-x) and y = x^2(7-x) cross when they are equal to each other

So

x(4-x) = x^2(7-x)

Expand and rearrange

4x - x^2 = 7x^2 - x^3

x^3 - 8x^2 + 4x = 0

Factorise

x (x^2 - 8x + 4)

Therefore solving this equation gives the x values of the roots where the 2 lines cross

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Thank you!!
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davros
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(Original post by fossilcollective)
y = x (4-x) and y = x^2(7-x) cross when they are equal to each other

So...
I know you're trying to be helpful, but please don't post full solutions in future - it's against forum rules!

We try to stick to giving hints and suggestions on this forum - this helps people to learn to solve problems for themselves with a nudge in the right direction.
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