Tìm GTNN lớp 9
tìm GTNN của :
a/ A = (x-1)(x-2)(x-5)(x-6)
b/ B = (x^2 - 1)(3x -10)(3x-16)
a/ A = (x-1)(x-2)(x-5)(x-6)
b/ B = (x^2 - 1)(3x -10)(3x-16)
giải:
a) A=
(x-1)(x-2)(x-5)(x-6)=(x-1)(x-6)(x-5)(x-2)
=(x2-7x+6)(x2-7x+10)=(t+6)(t+10) (với t=x2-7x)
=t2+16t+60=t2+2.8.t+64-4=(t+8)2-4≥-4
Vậy Amin=-4
khi t+8=0<=>x2-7x+8=0=>x=(7±√7)/2
b) B = (x2 - 1)(3x -10)(3x-16)
=(x+1)(x-1)
(3x -10)(3x-16)
=(x-1) (3x
-10)(3x-16)(x+1)
=(3x2-13x+10)(3x2-13x-16)
=(t+10)(t-16)
với (t=3x2-13x)
=t2-6t-160
=t2-2.3t+9-169
=(t-3)2-169≥-169
Vậy Bmin=-169
Khi t-3=0<=>3x2-13x-3=0=>x=(13±√133)/6
Trang Trước
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