Question

Докажите неравенство:

а). ( х – 2 )2 > х( х – 4 );

Answer 1

(x-2 )2 > x( x-4 ) \ 2x-4 > x^{2} -4x \ - x^{2} +2x+4x-4>0 \ - x^{2} +6x-4>0 |*(-1)\ x ^{2} -6x+4<0 \ D=36-16=20 \ sqrt{20} = sqrt{4*5}= 2sqrt{5} \ x1=(6+2sqrt{5}) /2=3+sqrt{5}) \ x2=(6-2sqrt{5}) /2=3-sqrt{5}) \