Question

Решите неравенство: (4 – 5x)^2=>(5 – 4x)^2

Answer 1

Ответ:

(-∞;-1]∪[1;+∞)

Пошаговое объяснение:

$(4-5x)^2\geq (5-4x)^2\\16-40x+25x^2\geq 25-40x+16x^2\\16-40x+25x^2-25+40x-16x^2\geq 0\\9x^2-9\geq 0\\9x^2\geq 9\\x^{2} \geq 1\\x^{2} -1\geq 0\\(x-1)(x+1)\geq 0\\x\geq 1\\x\leq -1$

(-∞;-1]∪[1;+∞)