Question

x^2+y^2-xy=3 and y-x=1,then xy/x^2+y^2=​

Answer 1

Answer:

The value of $\sf{\dfrac{xy}{x^{2}+y^{2}} \ is \ \dfrac{2}{5}.}$

Given:

The given equations are

x² + y² - xy = 3 and y - x = 1

To find:

• The value of $\sf{\dfrac{xy}{x^{2}+y^{2}}.}$

Solution:

》x² + y² - xy = 3...(1)

》y - x = 1...(2)

Squaring equation (2), we get

》x² + y² - 2xy = 1...(3)

Subtract equation (3) from equation (1), we get

⠀x² + y² - xy = 3

-

⠀x² + y² - 2xy = 1

_______________

⠀⠀⠀=> xy = 2...(4)

Substitute xy = 2 in equation (1), we get

⠀⠀⠀=> x² + y² - 2 = 3

⠀⠀⠀=> x² + y² = 5...(5)

Now,

$\sf{\longmapsto{\dfrac{xy}{x^{2}+y^{2}}=\dfrac{2}{5}}}$

Therefore, the value of $\sf{\dfrac{xy}{x^{2}+y^{2}} \ is \ \dfrac{2}{5}.}$