यदि `(x^(3)-y^(3)):(x^(2)+xy+y^(2))=5:1` और `(x^(2)-y^(2)):(x-y)=7:1`, तो अनुपात `2x : 3y` किसके बराबर है ?

Options

A. `3:2`
B. `2:3`
C. `4:3`
D. `4:1`

Answer

D

Explanation

(प्रश्ननुसार)
`(x^(3)-y^(3))/(x^(2)+xy+y^(2))=(5)/(1)`
`((x-y)(x^(2)+xy+y^(2)))/(x^(2)+xy+y^(2))=(5)/(1)`
x-y=5
`(x^(2)-y^(2))/(x-y)=(7)/(1)`
x+y=7
Solve equations (i) and (ii)
x=6
y=1
`therefore (2x)/(3y)=(2xx6)/(3xx1)=(12)/(3)=(4)/(1)`