Question

please answer by solving​

Answer 1

Answer:

B

Step-by-step explanation:

Let , x/y is the fraction.

According to question;

$x + y = 7$

$x = 7 - y$

assume it equation 1.

Also,

Now , the sum of the fraction and it's reciprocal is,

$\frac{x}{y} + \frac{y}{x} = \frac{29}{10}$

put the value of x from equation 1.

$\frac{7 - y}{y} + \frac{y}{7 - y} = \frac{29}{10} \\ \frac{{(7 - y)}^{2} + {y}^{2} }{7y - {y}^{2} } = \frac{29}{10} \\ \frac{49 + {y}^{2} - 14y + {y}^{2} }{7y - {y}^{2} } = \frac{29}{10} \\ 10( 2{y}^{2} - 14 + 49) = 29(7y - {y}^{2} ) \\ 20 {y}^{2} - 140y + 490 = 203y - 29 {y}^{2} \\ 20 {y}^{2} + 29 {y}^{2} = 203y + 140y - 490 \\ 49 {y}^{2} = 343y - 490 \\ 49 {y}^{2} -343y + 490 = 0$

Now solve this equation,

$49( {y}^{2} - 7y + 10) = 0 \\ {y}^{2} - 7y + 10 = 0 \\ {y}^{2} -5y - 2y + 10 = 0 \\ y(y - 5) - 2(y - 5) \\ (y - 2)(y - 5) = 0$

equate both with zero,

$y - 2 = 0 \\ y = 2 \:$

Or,

$y - 5 = 0 \\ y = 5$

put y=2 in equation 1,

$x = 7 - y \\ x = 7 - 2 \\ x = 5$

put y=5 in equation 1,

$x = 7 - y \\ x = 7 - 5 \\ x = 2$

therefore, when y =2 x is 5 and when y =5 x is 2,

So it have two solution either,

$\frac{2}{5} \: or \: \: \frac{5}{2}$

Hence , B is the right answer.

Have a nice day ahead.

Arsh❤️☺️