Question

if a+1/a=2, prove that a^2+1/a^2=a^4+1/a^4=a^3+1/a^3​

Answer 1

Answer:

Step-by-step explanation:

a + 1/a = 2

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

a^2 + 2 + 1/a^2 = 4

a^2 + 1/a^2 = 2

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

(a^2 + 1/a^2) (a + 1/a) = 2x2

a^3 + a + 1/a + 1/a^3 =4

a^3 +      2     + 1/a^3 =4

a^3 + 1/a^3 = 2

(a^2 + 1/a^2)(a^2 + 1/a^2) = 2x2

a^4 + 2 + 1/a^4 = 4

a^4 + 1/a^4 = 2

a + 1/a

= 2

= a^2 + 1/a^2

= a^3 + 1/a^3​

= a^4 + 1/a^4  (proved)