The numerator of a positive fraction is one more than twice the denominator. If the sum of the fraction and its reciprocal is $2.9$ ; find the fraction.
$\frac{25}{12}$
$\frac{5}{2}$
$\frac{9}{4}$
$\frac{2}{5}$

Question

The numerator of a positive fraction is one than twice the denominator- If the of the fraction and its reciprocal is 2-9- the fraction-dfrac -25-12-dfrac -5-2-dfrac -9-4-dfrac -2-5-

Toppr Admin · Accepted Answer

Letthefractionbe-xy-x-2y-1and-xy-yx-2-9-x2-y2xy-2-9x2-y2-2-9xy-2y-1-2-y2-2-9-2y-1-y4y2-4y-1-y2-2-9-2y2-y-4y2-4y-1-y2-2910-2y2-y-10-xD7-5y2-4y-1-58y2-29y50y2-40y-10-58y2-29y8y2-x2212-11y-x2212-10-08y2-x2212-16y-5y-x2212-10-08y-y-x2212-2-5-y-x2212-2-0-y-x2212-2-8y-5-0y-2andy-x2212-58-x2234-2y-1-2-xD7-2-1-5-x2234-number-52-

The numerator of a positive fraction is one more than twice the denominator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.2512529425

letthefractionbe(xy)x=2y+1and(xy)+(yx)=2.9(x2+y2xy)=2.9x2+y2=2.9xy(2y+1)2+y2=2.9(2y+1)y4y2+4y+1+y2=2.9(2y2+y)4y2+4y+1+y2=(2910)(2y2+y)10×(5y2+4y+1)=58y2+29y50y2+40y+10=58y2+29y8y2−11y−10=08y2−16y+5y−10=08y(y−2)+5(y−2)=0(y−2)(8y+5)=0y=2andy=(−58)∴2y+1=2×2+1=5∴number(52)

The numerator of a positive fraction is one more than twice the denominator. If the sum of the fraction and its reciprocal is $2.9$ ; find the fraction.
$\frac{25}{12}$
$\frac{5}{2}$
$\frac{9}{4}$
$\frac{2}{5}$

$letthefractionbe(xy)x=2y+1and(xy)+(yx)=2.9(x2+y2xy)=2.9x2+y2=2.9xy(2y+1)2+y2=2.9(2y+1)y4y2+4y+1+y2=2.9(2y2+y)4y2+4y+1+y2=(2910)(2y2+y)10×(5y2+4y+1)=58y2+29y50y2+40y+10=58y2+29y8y2−11y−10=08y2−16y+5y−10=08y(y−2)+5(y−2)=0(y−2)(8y+5)=0y=2andy=(−58)∴2y+1=2×2+1=5∴number(52)$