Question

Докажите неравенство:
х²+1≥2(3х-4)
х²+5≥10(х-2)​

Answer 1

Ответ:

x²+1≥2(3x-4)

x²+1≥6x-8

x²+1-6x+8≥0

x²+9-6x≥0

x²-6x+9≥0

(x-3)²≥0

x²+5≥10(x-2)

x²+5≥10x-20

x²+5-10x+20≥0

x²+25-10x≥0

x²-10x+25≥0

(x-5)²≥0