Question

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

Answer 1

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

Explanation:

Let the number be x

Given condition:

`\displaystyle x - (1)/(x) =(35)/(6) \\\\Subtract (35)/(6) \ to \ both \ sides\\\\x - (1)/(x) -(35)/(6) = 0\\\\Multiply \ 6x \ to \ both \ sides\\\\x * 6x - (1)/(x) * 6x -(35)/(6) * 6x = 0 * 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