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Grade: 12th pass

                        

if a+b+c=6 and a,b,c E R + then prove that 1/a+4/b+9/c>=6

3 years ago

Answers : (1)

Aditi singh
15 Points
							
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/c
So,1/a+4/b+9/c≥6 
Hence proved
1
2 years ago
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