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If \(x+\frac{1}{x}=7\), then what is the value of \(x^{2}+\frac{1}{x^{2}} + 1\)?

 Oct 10, 2019
 #1
avatar+105484 
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x + 1/x  = 7        square both sides

 

(x + 1x) (x + 1/x)  = 49

 

x^2  +  x (1/x)  + x (1/x)  +  1/x^2  = 49     

 

x^2  +  1  + 1  + 1/x^2  =  49     subtract  1 from both sides and rearrange the left side

 

x^2 + 1/x^2  + 1  =   48    Voila  !!!!

 

 

cool cool cool

 Oct 10, 2019

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