Solve the equation without using a calculator

Question

(x-2)(x+2)(x^2+4)=25x^2-16

Answer 1

Expand the left side of the equation.

 

(x² - 4)(x² + 4) = 25x² - 16

 

x⁴ - 16 = 25x² - 16

 

 

Bring all terms to the left side to make the right side equal to zero.

 

x⁴ - 25x² = 0

 

 

Factor out x².

 

x²(x² - 25) = 0

 

x²(x + 5)(x - 5) = 0

 

 

Set the three factors equal to zero and solve for x.