Question

The difference of a number and its reciprocal is 35/6 Find the number.

Answer 1

Answer:

$\huge\boxed{\sf x = 6 \ \ \ OR \ \ \ x = -1/6}$

Step-by-step explanation:

Let the number be x

Given condition:

$\displaystyle x - \frac{1}{x} =\frac{35}{6} \\\\Subtract \frac{35}{6} \ to \ both \ sides\\\\x - \frac{1}{x} -\frac{35}{6} = 0\\\\Multiply \ 6x \ to \ both \ sides\\\\x \times 6x - \frac{1}{x} \times 6x -\frac{35}{6} \times 6x = 0 \times 6x\\\\6x^2-6-35x=0\\\\6x^2-35x - 6 = 0$

Applying mid term break formula

• We can use the factor -36 and +1 to break the mid term (-35x) because multiplying -36 and +1 gives -36 which is the product of side terms (-6 * +6 = -36)

$6x^2-36x+x-6=0\\\\Take \ common\\\\6x(x-6)+1(x-6)=0\\\\Take \ (x-6) \ common\\\\(x-6)(6x+1)=0$

Either:

x - 6 = 0     OR    6x + 1 = 0

x = 6          OR      6x = -1

x = 6          OR       x = -1/6