Toán Lớp 7: Giải hộ gấp hứa cho hay nhất + tym và sao
Cho a/(2b)=b/(2c)=c/(2d)=d/(2a) (a,b,c,d>0)
Tính A=(2011a-2011b)/(c+d)+(2011b-2010c)/(a+d)+(2011c-2010d)/(a+b)+(2011d+2010a)/(b+c)
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Toán Lớp 7: Giải hộ gấp hứa cho hay nhất + tym và sao
Cho a/(2b)=b/(2c)=c/(2d)=d/(2a) (a,b,c,d>0)
Tính A=(2011a-2011b)/(c+d)+(2011b-2010c)/(a+d)+(2011c-2010d)/(a+b)+(2011d+2010a)/(b+c)
Comments ( 2 )
a/(2b)=b/(2c)=c/(2d)=d/(2a)=(a+b+c+d)/(2b+2c+2d+2a)=(a+b+c+d)/(2.(a+b+c+d))=1/2
Do đó:
{(a/(2b)=1/2=>2a=2b=>a=b),(b/(2c)=1/2=>2b=2c=>b=c),(c/(2d)=1/2=>2c=2d=>c=d),(d/(2a)=1/2=>2d=2a=>d=a):}
=>a=b=c=d
A=(2011a-2010b)/(c+d)+(2011b-2010c)/(a+d)+(2011c-2010d)/(a+b)+(2011d-2010a)/(b+c)
A=(2011a-2010a)/(a+a)+(2011a-2010a)/(a+a)+(2011a-2010a)/(a+a)+(2011a-2010a)/(a+a)
A=((2011-2010)a)/(2a)+((2011-2010)a)/(2a)+((2011-2010)a)/(2a)+((2011-2010)a)/(2a)
A=a/(2a)+a/(2a)+a/(2a)+a/(2a)
A=1/2+1/2+1/2+1/2
A=4/2
A=2
Vậy A=2