Question

the difference between a number and its reciprocal is 63 upon 8 find the number

Answer 1

$x - \frac{1}{x} = \frac{63}{8} \\ 8{x}^{2} - 63x - 8 = 0 \\ 8 {x}^{2} - 64x + x - 8 = 0 \\ 8x(x - 8) + 1(x - 8) = 0 \\ x = 8$

Answer 2

Given:

the difference between a number and its reciprocal is 63 upon 8

To Find:

Find the number

Solution:

It is given that the difference between a number and its reciprocal is 63/8, so let the number be x then we can formulate an equation that is,

$x-\frac{1}{x} =\frac{63}{8}$

Now simplifying it,

[tex]x-\frac{1}{x} =\frac{63}{8} \\ 8(x^2-1)=63x\\ 8x^2-63x-8=0[/tex]

Now we have a quadratic equation with us which can be solved by splitting the middle term, which goes as,

[tex]8x^2-63x-8=0\\ 8x^2-64x+x-8=0\\ 8x(x-8)+1(x-8)=0\\ (8x+1)(x-8)=0\\ x=\frac{-1}{8} or 8[/tex]

By splitting the term into 64 and 1 because 64*1=8*8 which is the defined rule for splitting a term in a quadratic equation.

Hence, the number is -1/8 or 8.