Question
4x^4+-3z=6
linear or non linear
linear or non linear
Answers
GPT-4o mini
The equation \( 4x^4 - 3z = 6 \) is a non-linear equation.
This is determined by the presence of the term \( x^4 \), which is a polynomial of degree 4. In general, an equation is considered linear if it can be expressed in the form \( ax + by + cz = d \) where \( a, b, c, \) and \( d \) are constants and the variables \( x, y, z \) are to the first power only (i.e., no variable is raised to a power greater than 1). Since the term \( x^4 \) violates this condition, the equation is classified as non-linear.
This is determined by the presence of the term \( x^4 \), which is a polynomial of degree 4. In general, an equation is considered linear if it can be expressed in the form \( ax + by + cz = d \) where \( a, b, c, \) and \( d \) are constants and the variables \( x, y, z \) are to the first power only (i.e., no variable is raised to a power greater than 1). Since the term \( x^4 \) violates this condition, the equation is classified as non-linear.