Toán Lớp 6: Cho a/b >0. CMR a/b+b/a > hoặc = 2
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Toán Lớp 6: Cho a/b >0. CMR a/b+b/a > hoặc = 2
Comments ( 2 )
a+b>=2\sqrt{ab}
+)Cm:
(a-b)^2>=0
<=>(a-b)(a-b)>=0
<=>a^2-2ab+b^2>=0
<=>a^2+b^2>=2ab
<=>a^2+2ab+b^2>=4ab
<=>(a+b)^2>=(\sqrt{4ab})^2
<=>a+b>=\sqrt{4ab}
<=>a+b>=\sqrt{2^2ab}
<=>a+b>=2\sqrt{ab}
+)Với a,b>0; Áp dụng bất đẳng thức Co-si (Cauchy) ta được :
a/b+b/a>=2\sqrt{(a)/(b).(b)/(a)}=2\sqrt{{ab}/{ab}}=2\sqrt{1}=2
=>a/b+b/a>=2
Vậy : a/b+b/a>=2