A system equation is-





Solve for real x and y .
How to solve it? Please explain. The question is correct.

Given that,

x⁴y⁵ + x⁵y⁴ = 810

➝ x⁴y⁴(x+y) = 810 ---(1)

Further given that,

x⁶y³ + x³y⁶ = 945

x³y³(x³y³) = 945

We know,

So, using this identity, we get,

➝ x³y³( x + y )( x² - xy + y²) = 945

---(2)

On dividing equation (1) and (2), we get,

➝ 6x² + 6y² = 13xy

➝ 6x² - 13xy + 6y² = 0

➝ 6x² - 4xy - 9xy + 6y² = 0

➝ 2x( 3x - 2y ) - 3y( 3x - 2y ) = 0

➝ ( 3x - 2y ) ( 2x - 3y ) = 0

In Substating the value of x in equation (1) we get,

On Substituting the value of y in equation (2), we get,

hi there!

the answer will be d: 2