Question

Please answer this question​

Answer 1

`\bold{\underline{\underline{\underbrace{Answer}}}}`

x = p and y = -q

Explanation:

• To find

The value of x and y

• Given

px + qy = p² - q²(equation 1)

qx - py = 2py

• Solution

{Taking equation 2}

`\sf qx - py = 2py`

{Taking py on RHS}

`\sf qx = 2py \ + py`

{Dividing both sides by q

`\sf x = (2pq)/(q) + (py)/(q) \\ \\ \sf x = 2p + (py)/(q) (equation \: 3)`

{Now substituting the value of equation 3 in equation 1}

`\sf p(2p + (py)/(q) ) + qy = {p}^(2) - {q}^(2) \\ \\ \sf 2 {p}^(2) + \frac{ {p}^(2)y }{q} + qy = {p}^(2) - {q}^(2)`

{Taking 2p² on RHS and taking LCM on LHS}

`\sf \frac{ {p}^(2)y + {q}^(2) y }{q} = {p}^(2) - {q}^(2) - 2 {p}^(2) \\ \\ \sf \frac{y( {p}^(2) + {q}^(2) ) }{q} = - ( {p}^(2) + {q}^(2) )`

{Dividing (p² + q²) both sides}

`\sf (y)/(q) = - 1 \\ \\ \red{ \boxed {\bold{y = - q}} }`

{Now using value of y in equation 3}

`\sf x = 2p - (pq)/(q) \\ \\ \sf x = 2p - p \\ \\ \red{ \boxed{ \bold{ x = p}}}`