how to solve 9=16x^4-85x^2

Question

they gave me the area of a rectangle which is 16x^4-81x^2 and the width is 4x^2+9 and im suppose to find the length and solve the equations . i dont know if i did it right

Answer 1

16x^4-81x^2=x^2(16x^2-81)=x^2(4x-9)(4x+9).

(4x^2+9)(4x^2-9)=16x^4-81, which is not quite 16x^4-81x^2! Check your question again. I suspect that the area of the rectangle was actually 16x^4-81, so that the width of 4x^2+9 is a factor and the length is 4x^2-9.