Question

the difference of two number is 8 and the difference of their reciprocal is 8/153 find both the number

Answer 1

x=17,-9 and Y= -17,9

Answer 2

Answer:

The two numbers are 4.5 and 3.5.

Step-by-step explanation:

Given : The difference of two number is 8 and the difference of their reciprocal is 8/153

To find : Both the number ?

Solution :

Step 1. Let x be one whole number and $\frac{1}{x}$ be its reciprocal.  

Step 2. Let 8-x be the other whole number and $\frac{1}{8-x}$ be its reciprocal.  

Step 3. Then, According to question

$\frac{1}{8-x}-\frac{1}{x}=\frac{8}{153}$

Step 4. Solving the equation by taking LCM in denominator

$\frac{x-(8-x)}{x(8-x)}=\frac{8}{153}$

$(2x-8)\times 153=8\times (8x-x^2)$

$306x-1224=64x-8x^2$

$8x^2+242x-1224=0$

$4x^2+121x-612=0$

Solve using quadratic formula,

General form - $ax^2+bx+c=0$

$D=b^2-4ac$  

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$  

Equation is $4x^2+121x-612=0$

where, a=4 , b=121, c=-612

$D=b^2-4ac$

$D=(121)^2-4(4)(-612)$

$D=24433$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-(121)\pm\sqrt{24433}}{2(4)}$  

$x=\frac{-121\pm\sqrt{24433}}{8}$  

$x=\frac{-121+\sqrt{24433}}{8},\frac{-121-\sqrt{24433}}{8}$

$x=4.413,-34.663$

Ignoring the negative solution,

Approximately x=4.5 one number

Other number is 8-x=8-4.5=3.5

Therefore, The two numbers are 4.5 and 3.5.