Question

If X+1/X=√5Then
x-1/X=?
x2-1/X2=?​

Answer 1

Step-by-step explanation:

1st squaring giving condition

by using 2nd formula of (a+b)^2=(a-b)^2+4ab

then we get the 1st result

for next we use the formula of a^2-b^2

and hence the result.....

Answer 2

Question:

If x + 1/x = √5, then find the value of :

• x - 1/x = ?
• x² - 1/x² = ?

Given:

• x + 1/x = √5......(I)

To find:

• x - 1/x = ?
• x² - 1/x² = ?

Solution:

• Since, x + 1/x = (√5)

(By squaring both sides)

=> ( x + 1/x )² = (√5)²

( By using ( a + b )² = a² + 2ab + b² )

=> x² + 2 × x × 1/x + 1/x² = 5

=> x² + 2 + 1/x² = 5

=> x² + 1/x² = 5 - 2

=> x² + 1/x² = 3

• Now, x² + 1/x² = 3

=> x² + 1/x² - 2 = 3 - 2

( By subtracting 2 from both sides)

=> x² + 1/x² - 2 × x × 1/x = 1

( There will be no change since x is going to be cancelled)

=> ( x - 1/x )² = 1

( By using ( a - b ) ² = a² - 2ab + b²)

=> ( x - 1/x ) = √1

( √1 is 1)

=> ( x - 1/x ) = 1.......(II)

Therefore, x - (1/x) = 1.

• Now, x² - 1/x² = ( x + 1/x ) ( x - 1/x )

( By using a² - b² = (a + b) (a - b))

=> x² - 1/x² = ( √5 ) (1)

( By putting the Values of ( x + 1/x ) = √5 from (I) and ( x - 1/x ) = 1 from (II))

=> x² - 1/x² = √5

Therefore, x² - 1/x² = √5.

Answer:

• x - 1/x = 1
• x² - 1/x² = √5