To solve the inequality, we can expand the terms and simplify:
(х^2-4х)^2-(x-2)^2-16 < 0(x^2 - 4x)(x^2 - 4x) - (x - 2)(x - 2) - 16 < 0(x^4 - 8x^3 + 16x^2) - (x^2 - 4x - 4) - 16 < 0x^4 - 8x^3 + 16x^2 - x^2 + 4x + 4 - 16 < 0x^4 - 8x^3 + 15x^2 + 4x - 12 < 0
Factorizing the equation is difficult given the complexity of the terms, so we can analyze it using a graphing calculator or software. This will allow us to determine the values of x that satisfy the inequality.
To solve the inequality, we can expand the terms and simplify:
(х^2-4х)^2-(x-2)^2-16 < 0
(x^2 - 4x)(x^2 - 4x) - (x - 2)(x - 2) - 16 < 0
(x^4 - 8x^3 + 16x^2) - (x^2 - 4x - 4) - 16 < 0
x^4 - 8x^3 + 16x^2 - x^2 + 4x + 4 - 16 < 0
x^4 - 8x^3 + 15x^2 + 4x - 12 < 0
Factorizing the equation is difficult given the complexity of the terms, so we can analyze it using a graphing calculator or software. This will allow us to determine the values of x that satisfy the inequality.