Question

if (a^2+1/a^2)=32 find (a^3+1/a^3)

Answer 1

Answer:

Step-by-step explanation:

The given equation is,

a^2 + 1/a^2 = 32

Add  2 on both sides

a^2 + 1/a^2 + 2 = 34

a^2 + 1/a^2 + 2 (a) (1/a) = 34     (since a*(1/a) =1)

(a + 1/a) ^2 = 34

a + 1/a = sqrt(34)

Now

(a + 1/a)^3 = 34^(3/2)

a^3 + 1/a^3 + 2a(1/a) (a + 1 /a) = 34^(3/2)

a^3 + 1 /a^3 + 2(1)(sqrt(34) = 34^(3/2)

a^3 + 1 /a^3  = 34^(3/2) - 2)(sqrt(34)

                    = 34^(1/2) * (34^3 - 2)

                    = 39302 * (34)^(1/2)