Question

Can you please give the separate equation of the equation${x^2} - 6xy + 8{y^2} = 0$.

Answer 1

Hint: In the above given question, we are asked to find out the separate equation for the given equation. Simplify the given quadratic equation in the simplest form possible by various manipulations.

Complete step-by-step answer:
We have the given equation as

${x^2} - 6xy + 8{y^2} = 0$

We can rewrite this equation as given below by splitting the equation into factors,

$ \Rightarrow {x^2} - 2xy - 4xy + 8{y^2} = 0$

$ \Rightarrow x(x - 2y) - 4y(x - 2y) = 0$

$ \Rightarrow (x - 2y)(x - 4y) = 0$

\[\therefore x = 2y,4y\]

Hence, the separate equation of the equation${x^2} - 6xy + 8{y^2} = 0$can be\[x = 2y,4y\].

Note: When we face such a type of problem, simply write the given quadratic equation and factorize it to reach the appropriate solution. Evaluate the equation upto the point, this equation can not be further evaluated anymore.