Question

if (a²+1/a²) = 27 find the value of (i) (a-1/a) (ii) (a³-1/a³)​

Answer 1

Answer:

5  and 140

Step-by-step explanation:

⇒ a² + 1/a² = 27

    Subtract 2 from both sides:

⇒ a² + 1/a² - 2 = 27 - 2

⇒ a² + (1/a)² - 2(a * 1/a) = 25

⇒ (a - 1/a)² = 25

⇒ a - 1/a = 5

        (i):   a - 1/a = 5

Cube on both sides of a -1/a = 5:

⇒ (a - 1/a)³ = 5³

⇒ a³ - (1/a)³ - 3(a*1/a)(a - 1/a) = 125

⇒ a³ - 1/a³ - 3(1)(5) = 125

⇒ a³ - 1/a³ - 15 = 125

⇒ a³ - 1/a³ = 140

Answer 2

$\huge \sf {a}^{3} - \frac{1}{ {a}^{3} } = 140$

for further explanation , refer the attachments