Question

IF x+1/x=4,find
(i) x²+1/x²
(ii) x-1/x
(iii) x³-1/x³
plz help
first one will be brainliest
PLZ WRITE CORRECT ASWER

Answer 1

Given : x + 1/x = 4

To find : (I) x² + 1/x²

(ii) x - 1/x

(iii) x³ - 1/x³

solution : as it is given that, x + 1/x = 4

squaring both sides we get,

(x + 1/x)² = 4²

⇒x² + 1/x² + 2 × x × 1/x = 16

⇒x² + 1/x² + 2 = 16

⇒x² + 1/x² = 14 ......(1)

(ii) we know, (a - b)² = (a + b)² - 4ab

⇒(x - 1/x)² = (x + 1/x)² - 4 × x × 1/x

⇒(x - 1/x)² = (4)² - 4

⇒(x - 1/x)² = 16 - 4 = 12

⇒(x - 1/x) = 2√3 .........(2)

(iii) we know, a³ - b³ = (a - b)³ + 3ab(a - b)

so, x³ - 1/x³ = (x - 1/x)³ + 3 × x × 1/x (x - 1/x)

= (2√3)³ + 3(2√3)

= 24√3 + 6√3 = 30√3

so, (x³ - 1/x³) = 30√3 .............(3)

Answer 2

(i) x²+1/x² = 14

(ii) x-1/x = 2√3

(iii) x³-1/x³ = 18√3

Step-by-step explanation:

Given: x+1/x = 4

Find: (i) x²+1/x²

(ii) x-1/x

(iii) x³-1/x³

Solution:

(i) x²+1 / x² = (x + 1/x)² - 2 from the expression (a+b)² = a² + b² + 2ab

       = 4² - 2

       = 16 - 2

      = 14

(ii) x - 1/x.

  (x - 1/x)² = (x + 1/x)² - 4 = 16- 4 = 12

   x - 1/x = root of 12 = 2√3

(iii) x³ - 1/x³ = (x - 1/x)³  - 3 (x - 1/x) = (2√3)³ - 3(2√3) = 24√3 - 6√3 = 18√3