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Converting square root to perfect square

  • Thread starter cstvlr
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  • #1
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Homework Statement



Hi,

I have a problem in my book in which they use a method of making sqrt( 36 + x^2 ) a perfect square by simply making x = 3( t - 1/t ) and then we get 9( t + 1/t )^2 by substituting back into sqrt(36 + x^2). My question is that why did the chose 3( t - 1/t ), is there a rule?

thanks in advance.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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What were they trying to do with the expression √(36+x2) ? For example, if they were trying to integrate, you could have made a simple trig substitution instead of trying to think of some odd set of functions to string together.
 
  • #3
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no its in an equation form,

C(x) = [(9-x) + 1.25sqrt( x^2 + 36 )], where C(x) is a function.

and they're trying to solve for x, so they used the method above, and I know how to solve it, but I lost it when they used let x = 3( t - 1/t )
 
  • #4
rock.freak667
Homework Helper
6,230
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no its in an equation form,

C(x) = [(9-x) + 1.25sqrt( x^2 + 36 )], where C(x) is a function.

and they're trying to solve for x, so they used the method above, and I know how to solve it, but I lost it when they used let x = 3( t - 1/t )
x = 3( t - 1/t ) ⇒ x2 = 9( t - 1/t )2

∴√(36+x2)=√(36+9(t- 1/t)2), how does that turn into an expression like √(a+b)2?

I do not think there rule per se for using that substitution though.
 
  • #5
12
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Fair enough, thanks anyway.
 

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