Question

please solve the above question

Answer 1

let x/y is the fraction ,
a/c to question,
y = 2x +1 ------(1)

x/y + y/x = 2.9

x/(2x +1) + (2x +1)/x = 2.9

x² + (2x +1)² = 2.9x (2x +1) = 5.8x² +2.9x

5x² +4x +1 = 5.8x² +2.9x

0.8x² -1.1x -1 = 0

8x² -11x -10 =0

8x² -16x +5x -10 = 0

8x (x -2) +5( x -2) = 0

(8x +5)(x -2) = 0

x =2, -5/8
but x ≠ -5/8

so, x = 2

so, y = 2x +1 = 2×2 +1 = 5

so, fraction = 2/5

Answer 2

let x/y is the fraction

A/Q,
y = 2x +1 ------(i)

x/y + y/x = 2.9
x/(2x +1) + (2x +1)/x = 2.9
x² + (2x +1)² = 2.9x (2x +1) = 5.8x² +2.9x
5x² +4x +1 = 5.8x² +2.9x
0.8x² -1.1x -1 = 0
8x² -11x -10 =0
8x² -16x +5x -10 = 0
8x (x -2) +5( x -2) = 0
(8x +5)(x -2) = 0

x =2 or x =  -5/8

but x ≠ -5/8  (as the fraction is positive)

So, x = 2

 y = 2x +1 = 2×2 +1 = 5

Therefore the required fraction is 2/5

Hope This Helps You!