SOLUTION: (a) Expand (a + 1/a)^2 (b) Given that a + 1/a =7, use your result in (a) to find the value of a^2 + 1/a^2

Algebra ->  Equations -> SOLUTION: (a) Expand (a + 1/a)^2 (b) Given that a + 1/a =7, use your result in (a) to find the value of a^2 + 1/a^2      Log On


   

Question 1038495: (a) Expand (a + 1/a)^2
(b) Given that a + 1/a =7, use your result in (a) to find the value of a^2 + 1/a^2
Answer by Othel(27) About Me  (Show Source):
You can put this solution on YOUR website!
In problem 'a' we are asked to expand the expression. So...
%28a%2Aa%29%2B%28a%2Fa%2Ba%2Fa%29%2B%281%2Fa%2A1%2Fa%29
which is...
a%5E2%2B2%2B1%2Fa%5E2
Problem 'b' states that the expression within parenthesis in problem 'a' is equal to 7, and squaring that equals 49.
so...
%28a%5E2%2B2%2B1%2Fa%5E2%29=49
In order to find the value of a%5E2%2B%281%2Fa%5E2%29, we subtract 2 from both sides of our previous equation.
a%5E2%2B1%2Fa%5E2=47
I hope this helps! Learn on