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Find a relation b/w x and y in order that rth mean between x and 2y is the same as the rth mean b/w 2x and Y, when n means are inserted in each case .

Find a relation b/w x and y in order that rth mean between x and 2y is the same as the rth mean b/w 2x and Y, when n means are inserted in each case .

Grade:12th pass

1 Answers

Arun
25750 Points
4 years ago
rth arithmetic mean b/w x and 2y : x + r*((2y-x)/(n+1))
rth arithmetic mean b/w 2x and y: 2x + r*((y-2x)/(n+1))
since both are equal
x + r*((2y-x)/(n+1)) =2x + r*((y-2x)/(n+1))
=> r * (((2y-x)-(y-2x))/(n+1)) = x
=> r*(x+y)/(n+1) = x

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