SOLUTION: if m - 1/m = 5; find: (i) m^2 + 1/m^2 (ii) m^4 + 1/m^4 (iii) m^2 - 1/m^2 I solved the first two but I am unable to solve no. (iii).

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Question 1104382: if m - 1/m = 5; find:
(i) m^2 + 1/m^2
(ii) m^4 + 1/m^4
(iii) m^2 - 1/m^2
I solved the first two but I am unable to solve no. (iii).
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
if m - 1/m = 5
-------------
Is it (m - 1)/m ?
Or m - (1/m) ?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
I will solve (iii) only. 

 = 5  ====>

m^2 - 5m - 1 = 0  ====>  (apply the quadratic formula)

 =  = .


In other words,    = ,   = .


Notice that    = -1.


You can check it by making direct calculations

    =  =  =  = -1,

or derive it from the Vieta's theorem.


Thus   =  =    and   =  = .


It implies    =  =  =  =  = ,   and

              =  =  =  =  = .


Thus you have

             = ,   = ,  which implies   -  = ,   and


             = ,   = ,  which implies   -  = ,

Answer.   If   - = 5,  then this equation has  TWO solutions;  correspondingly,  "m"  has  TWO values;

                correspondingly,    has  TWO values,   and,  correspondingly,   -  has two values   +/- .

Solved.



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