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
