Solving (1/2)x^4-x^2-1=0: A Comprehensive Guide

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To solve the equation (1/2)x^4 - x^2 - 1 = 0, substituting t = x^2 simplifies the problem. Multiplying both sides by 2 can eliminate fractions for easier manipulation. A common approach involves using "guess and check" to find an initial root, followed by polynomial long division to simplify the polynomial. This method allows for a more straightforward equation to solve afterward. Engaging with the problem by showing initial attempts is encouraged to facilitate discussion and assistance.
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(1/2)x^4-x^2-1=0
 
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try let t=x^2
by the way, you'd better show at least some of your attempt first, people do not like to answer a question shown in this way
 
Yes, let's see some work nameVoid!

Another hint, if you don't like fractions, is to multiple both sides of the equation by 2.


01
 
A popular strategy to get the first root to this type of problem is "guess and check". After you've guessed one root, which is easy to do in this case, you can do polynomial long division to reduce the order of the polynomial and get an equation you may be more familar with solving.
 

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