Question

If a^2+1/a^2=11, find the value of

(i) a^3-1/a^3 (ii) a^3+1/a^3

Answer 1

Step-by-step explanation:

first equation X cube minus one upon x is equal to x cube minus one upon a cube and a cube cancel it with a few the first equation answer is -1 and second a cube + 1 upon x cube 82 cancel is equal to 1 second equation answer

Answer 2

Answer:

(i) 36

(ii) 10√13

Solution:

Given: a² + 1/a² = 11

Solution for (i) :-

We have ;

=> a² + 1/a² = 11 ----------(1)

=> a² + 1/a² - 2 = 11 - 2 { subtracting 2 both sides }

=> a² - 2a×1/a + a² = 9

=> ( a - 1/a )² = 9

=> a - 1/a = √9

=> a - 1/a = 3 ---------(2)

Now,

=> a³ - 1/a³ = (a - 1/a)(a² + a×1/a + 1/a²)

=> a³ - 1/a³ = (a - 1/a)(a² + 1/a² + 1)

=> a³ - 1/a³ = 3(11 + 1) { using eq-(1) and (2) }

=> a³ - 1/a³ = 3×12

=> a³ - 1/a³ = 36

Solution for (ii) :-

We have ;

=> a² + 1/a² = 11 ----------(1)

=> a² + 1/a² + 2 = 11 + 2 { adding 2 both sides }

=> a² + 2a×1/a + a² = 13

=> ( a + 1/a )² = 13

=> a + 1/a = √13

=> a + 1/a = √13 --------(2)

Now,

=> a³ + 1/a³ = (a + 1/a)(a² - a×1/a + 1/a²)

=> a³ + 1/a³ = (a + 1/a)(a² + 1/a² - 1)

=> a³ + 1/a³ = √13(11 - 1) { using eq-(1) and (2) }

=> a³ + 1/a³ = √13×10

=> a³ + 1/a³ = 10√13