Given that, H³- H -1 = 0.

Determine analytically the exact value of:

(3H² - 4H)^1/3 + H(2H²+3H+2)^1/4

I took  (H^3)^(1/3) = (H-1)^(1/3) to get:

H = (H+1)^(1/3)  Then used excel to iterate.  ( I started by puting 1 in for H on the right side.  Then took the solution and put it back into H until I got approximately what I put in.)  I stoped at H = 1.324718.

With this I got a solution of x= 2.00000063 or just 2 <TABLE style="WIDTH: 58pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=77 border=0 x:str> <COLGROUP> <COL style="WIDTH: 58pt; mso-width-source: userset; mso-width-alt: 2816" width=77> <TBODY> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 58pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right width=77 height=17 x:num="2.0000006304371531"></TD></TR></TBODY></TABLE>

Posted by Brett Stripe on 2007-01-23 11:51:08