Question

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

Answer 1

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