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if a+b+c=6 and a,b,c E R + then prove that 1/a+4/b+9/c＞=6 if a+b+c=6 and a,b,c E R+ then prove that 1/a+4/b+9/c＞=6
a+b+c=6 can also be written as a+b/2+b/2+c/3+c/3+c/3=6 so, according to the formula of AM≥HM which is a+b+c÷3≥3÷1/a+1/b+1/c. So, here a+b/2+b/2+c/3+c/3+c/3÷6≥6÷1/a+4/b+9/c 6÷6≥6÷1/a+4/b+9/c (according to data)1≥6÷1/a+4/b+9/cSo,1/a+4/b+9/c≥6 Hence proved1
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