+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 \(\sqrt{7-\sqrt{13}} - \sqrt{7+\sqrt{13}}\)
+128474 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
+2401 2.
a + b = 14
ab = 46
(a+b)^2 - 2ab = a^2 + b^2
Take it from here. :))
=^._.^=
