Question

Решите неравенство $(5x-9)^2geq (9x-5)^2$

Answer 1

$(5x-9)^2geq (9x-5)^2\\(5x-9)^2-(9x-5)^2geq 0; ; qquad Big[; A^2-B^2=(A-B)(A+B); Big]\\Big ((5x-9)-(9x-5)Big)Big((5x-9)+(9x-5)Big)geq 0\\(5x-9-9x+5)(5x-9+9x-5)geq 0\\(-4x-4)(14x-14)geq 0\\-4cdot (x+1)cdot 14(x-1)geq 0\\(x+1)(x-1)leq 0\\znaki:; ; ; +++[-1; ]---[; 1; ]+++\\xin [-1, ;, 1; ]$