If the coefficient of x in (kx+2/k)^2 - (3x + 1/k)^3 is 0 then find the value(s) of k

Question

If the coefficient of x in (kx+2/k)^2 - (3x + 1/k)^3 is 0 then find the value(s) of k

Answer 1

(kx+2/k)² - (3x+1/k)³ =

 

    k²x² + 4x + 4 / k² - 27x³ - 3(3x)²(1/k) - 3(3x)(1/k)² - 1/k³

 

So, 4 - 9/k² = 0

 

           9/k²= 4

 

             k² = 9/4     k = ±3/2