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Q) n arithmetic means are inserted between x and 2y and then between 2x and y. If the rth means in each case be equal , then find the ratio x/y.
Asked by Anish | 14 Apr, 2019, 02:49: AM
answered-by-expert Expert Answer
L e t space x comma space A 1 comma space A 2 comma space � space A n comma space 2 y space b e space i n space A P. space space T h e n space c o m m o n space d i f f e r e n c e space equals space left parenthesis 2 y space minus space x right parenthesis divided by space left parenthesis n space plus space 1 right parenthesis space space A r space equals space x space plus space r d space equals space x space plus space r space left parenthesis 2 y space minus space x right parenthesis divided by space left parenthesis n space plus space 1 right parenthesis space equals space left square bracket x space left parenthesis n space plus space 1 right parenthesis space plus space r left parenthesis 2 y space minus space x right parenthesis right square bracket divided by space left parenthesis n space plus space 1 right parenthesis space N o w space 2 x comma space B 1 comma space B 2 comma space � space B n comma space y space a r e space i n space A P. space space T h e n space c o m m o n space d i f f e r e n c e space equals space left parenthesis y space minus space 2 x right parenthesis divided by space left parenthesis n space plus space 1 right parenthesis space space B r space equals space x space plus space r d space equals space x space plus space r space left parenthesis y space minus space 2 x right parenthesis divided by space left parenthesis n space plus space 1 right parenthesis space equals space left square bracket x space left parenthesis n space plus space 1 right parenthesis space plus space r left parenthesis y space minus space 2 x right parenthesis right square bracket divided by space left parenthesis n space plus space 1 right parenthesis space space S i n c e comma space A r space equals space B r comma space w e space h a v e colon space space left square bracket x space left parenthesis n space plus space 1 right parenthesis space plus space r left parenthesis 2 y space minus space x right parenthesis right square bracket divided by space left parenthesis n space plus space 1 right parenthesis space equals space left square bracket x space left parenthesis n space plus space 1 right parenthesis space plus space r left parenthesis y space minus space 2 x right parenthesis right square bracket divided by space left parenthesis n space plus space 1 right parenthesis space space O n space s i m p l i f y i n g comma space w e space g e t comma space r y space equals space x left parenthesis n space minus space r space plus space 1 right parenthesis H e n c e comma space x divided by y equals r divided by left parenthesis n minus r plus 1 right parenthesis.
Answered by Renu Varma | 14 Apr, 2019, 04:16: PM

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