`(0.9xx0.9xx0.9+0.2xx0.2+xx0.2+0.3xx0.3xx0.3-0.3xx0.9xx0.2xx0.3)/(0.9xx0.9+0.2xx0.2+0.2xx0.3xx0.3-0.9xx0.2-0.2xx0.3-0.3xx0.9)` का मान क्‍या है?

Options

A. `1.4`
B. `0.054`
C. `.8`
D. `1.0`

Answer

A

Explanation

According to the question
`(0.9xx0.9xx0.9+0.2xx0.2xx0.2+0.3xx0.3xx0.3-3xx0.9xx0.2xx0.3)/(0.9xx0.9+0.2xx0.2+0.3xx0.3-0.9xx0.2-0.2xx0.3-0.3xx0.9)`
As we know that
`a^(3)+b^(3)+c^(3)-3abc=(a+b=c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`((0.9)^(3)+(0.2)^(3)+(0.3)^(3)-3xx0.9xx0.2xx0.3)/((0.9)^(2)+(0.2)^(2)+(0.3)^(2)-0.9xx0.2xx0.3-0.3xx0.9)`
`implies((0.9+0.2+0.3)[(0.9)^(2)+(0.2)^(2)+(0.3)^(2)-0.9xx0.2-0.2xx0.3-0.3xx0.9])/((0.9)^(2)+(0.2)^(2)+(0.3)^(2)-0.9xx0.2-0.2xx0.3-0.3xx0.9)`
`implies 0.9+0.2+0.3=1.4`