1.

यदि `x=sqrt(5)+2` है तो `(2x^(2)-3x-2)/(3x^(2)-4x-3)` का मान ज्ञात करें।A. 0.1785B. 0.525C. 0.625D. 0.785

Answer» Correct Answer - C
`x=sqrt(5)+2` हर का परिमेयकरण
`implies 1/x=1/(sqrt(5)+2)xx(sqrt(5)-2)/(sqrt(5)-2)`
`implies (sqrt(5)-2)/(5-4)=sqrt(5)-2`
`implies x-1/x=sqrt(5)+2-sqrt(5)+2=4`
`:. (2x^(2)-3x-2)/(3x^(2)-4x-3)`
Multiply by `1/x` in numerator and denominator
`((2x^(2))/x-2/x-(3x)/x)/((3x^(2))/x-3/x-(4x)/x)implies(2x-2/x-3)/(3x-3/x-4)`
`=(2(x-1/x)-3)/(3(x-1/x)-4)implies (2xx4-3)/(3xx4-4)`
`=(8-3)/(12-4)=5/8=0.625`


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