Quick question - angles between two lines (1 Viewer)

[blackops23]

Q. The angle between the line y=x/A and the tangent to the curve y=Ax^2 at x=1 is 45 degrees

Find the value(s) of A
----------------------
Here's what I did

gradient of y=x/A is 1/A

Also y=Ax^2 --> dy/dx = 2Ax --> at x=1, gradient = 2A

so tan(45) = |(2A - 1/A)/(1+2)
=|(2A^2 - 1)/(3A)|

therefore:

3A = 2A^2 - 1
2A^2 - 3A - 1 = 0 ----1

OR

-3A = 2A^2 - 1
2A^2 + 3A - 1 = 0 -----2


Upon solving these equations I get non-simple answers -- did I do everything correctly or is there something wrong, because I was expecting the value of A to be a nice integer...

thanks guys

 

[kooliskool]

well, you did nothing wrong, it's either the question was wrong in the first place or that is the answer.

 

[someth1ng]

I often find that they want you to leave answers like these in exact value eg [3+sqrt(17)]/4

 

[kooliskool]

yep, that's right, unless told otherwise (e.g. rount to the nearest 2 dp), you are suppose to leave it as exact value.