Question

Eliminate x from x+1/x=2p , x-1/x=2q+1

Answer 1

Answer:

2q + 1 = 2p or 2q + 1 = - 2p

Step-by-step explanation:

Given---> x + 1 / x = 2 p and x - 1 / x = 2q + 1

To find ---> Eliminate x from given equation.

Solution--->We know that

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

ATQ,

x + 1 / x = 2p

Squaring both sides we get,

=> ( x + 1 / x )² = ( 2 p )²

Applying first formula, we get,

=> x² + 1 / x² + 2 ( x ) ( 1 / x ) = 4p²

=> x² + 1 / x² + 2 = 4p²

=> x² + 1 / x² = 4p² - 2 ...................( 1 )

ATQ, x - 1 / x = 2q + 1

Squaring both sides we get,

=> ( x - 1 / x )² = ( 2q + 1 )²

Applying second formula , we get,

=> x² + 1 / x² - 2 x ( 1 / x ) = 4q² + 1 + 4q

=> x² + 1 / x² = 4q² + 4q + 1 ..................( 2 )

By equation ( 1 ) and ( 2 ) , we get,

4q² + 4q + 1 = 4p²

=> ( 2 q + 1 )² = ( 2p )²

Taking square root of both sides we get,

=> ( 2q + 1 ) = ± 2p

Taking + sign we get,

2q + 1 = 2p

Taking ( - ) sign we get

2q + 1 = -2p