if (x/a+2b+c)=(a/b+2c+2a)=(2/c)+2a+2b)then show that each ratio =(x+y-2)/(a+b+3c)
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ba+b=a+c−bb+c−a=a+b+c2a+b+2c
or, 2b2(a+b)=a+c−bb+c−a=2(a+b+c)2(2a+b+2c)
=2b+a+c−b+2a+2b+2c2a+2b+b+c−a+4a+2b+4c (by addendo process)
=3a+3b+3c5a+5b+5c
=3(a+b+c)5(a+b+c)=35[∵a+b+c≠0]
∴ba+b=35 or, 5b+3a+3b or, 5b−3b=3a.
or, 2b=3a or, ab=23 or, a2=b2 ..(1)
Again, a+c−bb+c−a=35 or, 5a+5c−5b=3b+3c−3a
or, 5a+3a−5b−3b=3c−5c
or, 8a−8b=−2c or, 8a−12a=−2c[∵2b=3a]
or, −4a=−2c or, a−2=c−4 or , a−2=c−4 or, a2=c4 ..(2)
From (1) and (2) we get , a2=b3=c4.
Hence a2=b3=c4
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