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):
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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