Question

a) ( 2x-1)^2014 = ( 2x-1)^2016

b) 2^x+1 . 3^y= 12^x

c)10^x : 5^y= 20^y

Answer 1

(2x-1)^2014=(2x-1)^2016

(2x-1)^2016-(2x-1)^2014=0

(2x-1)^2014[(2x-1)^2-1)]=0

=> (2x-1)^2014=0, (2x-1)^2-1=0

2x-1=0, (2x-1)^2=1

2x=1, 2x-1=1, 2x-1=-1

x=1/2, 2x=2, 2x=0

x=1/2, x=1, x=0.

b/ 2^x+1.3^y=12^x

2^x+3^y=12^x

2^x=12^x-3^y. Vậy 2^0=12^0-3^y. (Vì nếu x,y>1 thì 12^x-3^y lẻ mà 2^x chẵn nên vô lí) => 1=1-3^y => 0=3^y (Vô lí vì 3^y>=1). Vậy ko có x,y thỏa mãn.

c/ 10^x:5^y=20^y

10^x=100^y

10^x=10^2y

=> x=2y. => xEN, y=2x