Question

[Bunn Chảnh Choẹ]

cho a,b,c,d,e,f nguyen d­uong sao cho: a/b>c/d>e/f ; af - be = 1

c/m: d > b+f

Answer 1

[Băng băng]

d= d* 1

= d* (af- be)

= daf- dbe

= daf- bcf+ bcf- dbe 

= f (ad- bc)+b (cf- de)

Do ab  >cd  >eƒ  nên ad- bc >=af- be=1, cf- de>=1

=> f(ad- be)+ b(cf- de) >= f + b

<=> d >= b+f (đpcm)