+67 1. Suppose \(a+\frac{1}{a} =3\),
a) Find \(a^2 +\frac{1}{a^2}\)
b) Find \(a^4 +\frac{1}{a^4}\)
c) Find \(a^3 + \frac{1}{a^3}\)
2. I'm thinking of two numbers. The sum of my numbers is 14 and the product of my numbers is 46. What is the sum of the squares of my numbers?
3. Simplify \(\sqrt{7-\sqrt{13}} - \sqrt{7+\sqrt{13}}\)
+129899 First one
(a)
(a + 1/a)^2 = a^2 + 2a (1/a) + 1/a^2 = 3^2
a^2 + 2 + 1/a^2 = 9
a^2 + 1/a^2 = 7
(b)
a^4 + 1/a^4
(a^2 + 1/a^2)^2 = a^4 + 2 a^2 (1/a^2) + 1/a^4 = 49
a^4 + 2 + 1/a^4 = 49
a^4 + 1/a^4 = 47
(c)
a^3 + 1/a^3 = (a + 1/a) ( a^2 - a(1/a) + 1/a^2) =
(3) ( a^2 + 1/a^2 - 1) =
(3) ( 7 - 1) =
18
+2407 2.
a + b = 14
ab = 46
(a+b)^2 - 2ab = a^2 + b^2
Take it from here. :))
=^._.^=
