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A Value Problem (Posted on 2007-01-14) Difficulty: 3 of 5
Given that, H3- H -1 = 0.

Determine analytically the exact value of:

(3H2 - 4H)1/3 + H(2H2+3H+2)1/4

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Different way | Comment 2 of 3 |

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
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