Question

if a^2+1/a^2 is equal to 11 then find a^3+1/a^3​

Answer 1

Ans:- a^2+1/a^2 = 11

= (a + 1/a)^2 - 2×a×1/a = 11

= (a + 1/a)^2 = 13

= a + 1/a = √13

now,

a^3+1/a^3 = (a + 1/a)(a^2 - a×1/a + 1/a^2)

= √13(11 - 1)

= 10√13

OR

(a + b)^3 = a^3 + b^3 + 3ab(a + b)

(a + 1/a)^3 = a^3 + 1/a^3 + 3×a×1/a(a + 1/a)

(√13)^3 = a^3 + 1/a^3 + 3×√13

13√13 = a^3 + 1/a^3 + 3√13

a^3 + 1/a^3 = 13√13 - 3√13 = 10√13

here is your answer

hope it will help you