How would you solve this equation?

Question

4x^2+9xy+5y^2=0

Answer 1

4x² + 9xy + 5y² = 0

4x² + 4xy + 5xy + 5y² = 0

Take out common term 4x and 5y

4x(x + y) + 5y( x + y) = .0

(x + y)(4x + 5y) = 0

x + y = 0 and 4x + 5y = 0

Substitute 4(x + y) = 0 in the equation 4x + 4y + y = 0

Therefore 0 + y = 0

y = 0

Substitute y= 0 in the equation x + y = 0

x + o = 0

x = 0.

 

 

 

Comments

The equation 4x² + 9xy + 5y^2=0

Compare it to homogeneous equation Ax² + Bxy + Cy² + F = 0

In this case  F = 0 ,we have trival solution x = 0 and y = 0.

The equation 4x² + 9xy + 5y²=0 represented  by two lines in the plane xy intersecting at the point (0,0).