Đáp án:
$\rm@sbpro2009$
Giải thích các bước giải:
`13`
`a)1+2+3+...+x=45`
`=>((x+1).x)/2=45`
`=>(x+1).x=90`
`=>(x+1).x=10.9`
`=>(x+1).x=(9+1).9`
`=>x=9`
Vậy `x=9`.
`b)(x+1)+(x+2)+(x+3)+...+(x+100)=5750` (Có `((x+100)-(x+1))/1+1=100` số hạng).
`=>100x+(1+2+3+...+100)=5750`
`=>100x+((100+1).100)/2=5750`
`=>100x+101.50=5750`
`=>100x+5050=5750`
`=>100x=700`
`=>x=7`
Vậy `x=7`.
`14`
`a)A=199.201`
`=>A=(200-1).201`
`=>A=200.201-201`
`=>A=200.(200+1)-201`
`=>A=200.200+200-201`
`=>A=200.200-1`
`=>200<300`
`=>200.200<300.200`
`=>A=200.200-1<300.200B`
`=>A<B`
Vậy `A<B`.
`b)C=35.53-18`
`=>C=(34+1).53-18`
`=>C=53.34+53-18`
`=>C=53.34+35`
`=>C=53.34+35=D=35+53.34`
`=>C=D`
Vậy `C=D`.
`c)E=2012.2016`
`=>E=(2014-2).2016`
`=>E=2014.2016-2.2016`
`=>E=2014.(2014+2)-2.2016`
`=>E=2014.2014+2.2014-2.2016`
`=>E=2014.2014-2.2`
`=>E=2014.2014-4`
`=>E=2014.2014-4<2014.2014=P`
`=>E<P`
Vậy `E<P`.
`d)G=25.33-10`
`=>G=(26-1).33-10`
`=>G=26.33-33-10`
`=>G=26.33-43`
`=>33<53`
`=>26.33<26.53`
`=>G=26.33-10<53.26+10=H`
`=>G<H`
Vậy `G<H`.
`e)M=32.53-31`
`=>M=(31+1).53-31`
`=>M=31.53+53-31`
`=>M=31.53+22`
`=>22<32`
`=>M=31.53+22<31.53+32=N`
`=>M<N`
Vậy `M<N`.
`f)P=1990.2010`
`=>P=(2000-10).2010`
`=>P=2000.2010-10.2010`
`=>P=2000.(2000+10)-10.2010`
`=>P=2000.2000+10.2000-10.2010`
`=>P=2000.2000-10.10`
`=>P=2000.2000-100`
`=>P=2000.2000-100<2000.2000=Q`
`=>P<Q`
Vậy `P<Q`.