SOLUTION: If a+1/a=2 find 9a^2+1/a^2

Algebra ->  Equations -> SOLUTION: If a+1/a=2 find 9a^2+1/a^2      Log On


   

Question 1206133: If a+1/a=2 find 9a^2+1/a^2
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If a+1/a=2 find 9a^2+1/a^2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If  a + 1%2Fa = 2,  then

    a^2 + 1 = 2a   (after multiplying both sides by "a")

    a^2 - 2a + 1 = 0,

    (a-1)^2 = 0.


Hence,  a = 1.


Then  9a%5E2 + 1%2Fa%5E2 = 9%2A1%5E2 + 1%2F1%5E2 = 9 + 1 = 10.


ANSWER.  If  a + 1%2Fa = 2,  then  9%2Aa%5E2 + 1%2Fa%5E2 = 10.

Solved.