--------- Multiplying by LCD, a
 ---- Squaring each side

 ------- Dividing by a

OR

 ---- Squaring each side

 ------- Multiplying by a
 

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
 .





If sqrt(5)= 2+ 1/a, show that a= 4+1/a

~~~~~~~~~~~~~~~~~~~~~~~~







If  = 2 + ,  then   =      (1)


It implies   a =     (2)


Rationalize the denominator in the right side of (2):


a =  = . =  =  = .   (3)


Now in the formula  a = 4 +     (*)


    the left  side is  a =     (according to (3))


    the right side is  4 +  =  (now replace  by , based on (1), to get )  = 4 +  = .


Thus the both sides of (*) are the same.


The statement is proved.




 

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!
 


(1) Rewrite the given equation as , and rewrite the equation to be shown as 


(2) Solve the given equation to find a.







(3)  

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