यदि `5x+9y=5` और `125x^(3)+729y^(3)=120` है तो `x` तथा `y` का गुणनफल का मान क्या होगा?

Options

A. 45
B. `1//9`
C. `1//135`
D. `135`

Answer

C

Explanation

Given
`5x+9y=5` …………i
`125x^(3)+729y^(3)=120`……………ii
From equation i cubing both sides
`=(5x+9y)^(3)=5^(3)`
`implies 125x^(3)+729y^(3)+3xx5x xx 9y`
`(5x+9y)=125`
`implies 125x^(3)+729y^(3)+125xy xx 5-126`
`implies 120+135 xy xx 5=125`
`implies 135xy xx 5=5`
`implies xy=1/135`
`implies` Therefore produce of `x` and `y=1/135`