solve the equation by making an appropriate substiution

Question

4x⁴= 85x²-441

Answer 1

4x⁴ - 85x² + 441 = 0

 

4(x²)² - 85(x²) + 441 = 0

 

Let u = x²

 

So, in terms of u, the equation is:  4u² - 85u + 441 = 0

 

                                                 (4u - 49)(u - 9) = 0

 

                                                                   u = 49/4 or u = 9

 

Since u = x², we have x² = 49/4 or x² = 9

 

                               x = ±√(49/4), ±√9

 

                               x = ±7/2, ±3

Answer 2

First, subtract 85x² and add 441 on both sides of the equation.

 

4x⁴ - 85x² + 441 = 0

 

 

Let   x⁴ = q²

 

 

then  x² = q

 

 

 

so

 

4q² - 85q + 441 = 0

 

 

Use the quadratic formula to solve for q.  Once you have your values of q, plug them into this equation.

 

x = √q

 

 

to get your x.