The Student Room Group

FP2 - Hyperbolic functions question

It's the OCR (not MEI) Jan 08 paper question 8:

My problem is on part iii)
I get:
sinh3x=4sinhxsinh{3x}=4sinhx
3sinhx+4sinh3x=4sinhx3sinhx + 4sinh^3x=4sinhx
sinhx(4sinh2x1)=0sinhx(4sinh^2x-1)=0
sinhx=±12sinhx=\pm \frac{1}{2}
e2xex1=0e^{2x}-e^x-1=0 ( for +1/2)
ex=12(1±5)e^x=\frac{1}{2}(1\pm\sqrt5)
x=ln(12+52)x=\ln{(\frac{1}{2} + \frac{\sqrt5}{2})}

but there's another answer and I'm not sure how to get it. If you try and get a quadratic in e^x using the -1/2 answer instead of +1/2, the discriminant is <0.

;<
(edited 12 years ago)
Using -1/2, you should still get a real answer (I believe it's ln[(sqrt(5)-1)/2])
Reply 2
oh yeah of course, stupid mistake, my bad, thanks!
Reply 3
this is making me really nervous :biggrin:
Reply 4
Original post by kogaht
this is making me really nervous :biggrin:


sorry!:>

Quick Reply

Latest