доведiть нерiвнiсть (x+3)(x-10)<(x-5)(x-2)

Question

доведiть нерiвнiсть (x+3)(x-10)<(x-5)(x-2)</p>

Answer 1

x^2-10x+3x-30=0
x^2-7x-30=0

D = 49-4*(-30)- 49+120=169

x1= (7-13)/2=-3

x2=(7+13)/2=10

x=(1+3)(1-10)=-30

______________________
x^2-2x-5x+10=0

x^2-7x+10=0

D= 49-4*10=9

x1=(7-3)/2=2

X2= (7+3)/2=5

x=(1-2)(1-5)=10

 

Т.к. -30<10, то нер-во доказано</p>