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Solve sqrt(x^2 + 1) + x^2 + 1 = 90.

 May 4, 2020
 #1
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sqrt (x^2 + 1) + (x^2 + 1)  = 90

 

Let  u  =   sqrt (x^2 + 1)

And u^2  =(x ^2 + 1)

 

So  we  have

 

u + u^2  =  90          rearrange  as

 

u^2  + u  -  90    =   0      factor

 

(u + 10)  ( u - 9)   =   0

 

Set each factor to  0  and solve for u  and we have that

 

u = -10            u  = 9

 

This  means  that

 

sqrt (x^2 + 1)   = -10        this  has no real solutions

  

         or

sqrt (x^2 + 1)  =  9          square both sides

 

x^2  + 1   = 81      subtract 1 from both sides

 

x^2  = 80      take both roots

 

x = ±√80

 

x = ±4√5

 

 

 

cool cool cool

 May 4, 2020

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