Question

if x + 1/x =6, find the values of (i) x2 -1/x2 (ii) x-1/x​

Answer 1

Answer:

(i) ± 24√2

(ii) ± 4√2

Step-by-step explanation:

Find the value of x - 1/x first

x + 1/x = 6

Using algebraic identity (a - b)² = (a + b)² - 4ab

(x - 1/x)² = (x + 1/x)² - 4(x)(1/x)

(x - 1/x)² = 6² - 4(x)(1/x)

(x - 1/x)² = 36 - 4 = 32

Taking square root on both sides

x - 1/x = ± √32 = ± 4√2

Therefore the value of x - 1/x is ± 4√2

Now, x² - 1/x² = x² + ( 1/x )²

= ( x + 1/x )( x - 1/x )

Since a² - b² = (a + b)(a - b)

= 6( ± 4√2 )

= ± 24√2

Therefore the value of x² - 1/x² is ± 24√2.

Answer 2

Answer:

(i) +_ 4root over 2

(ii) +_ 24root over 2