C1 solving equations using a graph

Hey guys,

I'm trying to revise but I'm a bit stuck...

Wondering if anyone could help walk me through part B) of this question...

I'm pretty sure they want me to draw a straight line of some sort...

But how?

I don't know where to start....

I would really appreciate any help and guidence

thanks guys!

Like, ive read the mark scheme and I know I need to make the graph x + 1/x = 4-x

and then I need to draw the line y=4-x on the graph and find where it intersects the curve...

I just really don't understand why I need to do this, and how to see that i need to do this in the future..

Like how do I know to go from the first equation to getting x+1/x=4-x

can someone help me understand :frown:

(

Reply 2

samb1234

Well they've drawn out the graph of x+1/x for you. This implies that they want you to turn any equations they give you into the form x+1/x=y. If you subtract x from both sides of part b you get (2-1)x +1/x=4-x. Therefore x+1/x=4-x. If you then plot the line 4-x the intersections will be the solution(s).

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Reply 3

Kevin De Bruyne

Original post by wednesday_adams

Can you spot the difference between the equation of the graph you're given and the inequality?

What does setting the equations of two different lines give when you solve it?

Reply 4

wednesday_adams

Original post by SeanFM

Can you spot the difference between the equation of the graph you're given and the inequality?

What does setting the equations of two different lines give when you solve it?

and i got 0.3 and 1.7

Reply 5

Kevin De Bruyne

Original post by wednesday_adams

and i got 0.3 and 1.7

Apologies - I meant in general for my last question. If you have y = ... and y = ... what do you find when you make them equal and solve the equation?

And what's the difference between x + (1/x) = 4 and 2x + (1/x) = 4? This may help you to understand why they have done what they did in the mark scheme (setting those two equations equal to eachother).

(edited 9 years ago)

Reply 6

wednesday_adams

Original post by SeanFM

thanks for responding to me :smile:

do you mean if I set 2x + 1/x -4 = x + 1/x

so I would end up with 4-x = 0

?

Reply 7

Kevin De Bruyne

Original post by wednesday_adams

thanks for responding to me :smile:

do you mean if I set 2x + 1/x -4 = x + 1/x

so I would end up with 4-x = 0

?

Almost

I was trying to hint that 2x + 1/x = 4 is the same as x + (x + 1/x) = 4.

You already have a graph of y = (x + 1/x), so what possible graph could you draw to find all the points where 2x + 1/x = 4? Well, that's the same as x + (x + 1/x) = 4, which is the same as (x + 1/x) = 4 - x. So any x values satisfying that equation will give you the x values that satisfy 2x + 1/x = 4, because they are the same equation.

So can you see why they have to draw 4 - x?

I totally get why it's one of those questions where it's like 'yeah but how am I going to see that next time?'. Well, if it's the same question but with a different graph then the idea is the same - just get the equation of the graph you're given on the one side, and the equation of the graph that you have to draw on the other.