Question

The product of a positive number, its square, and its reciprocal is `100/81`. What is the number?

Please help...Thanks!!!

Answer 1

The 10 divided by 9

Explanation:

The equation for this problem would be

`x xx x^2 xx 1/x = 100/81` This reduces to

`x^2 = 100/81` Take the square root of both sides gives

`x = 10/ 9`

Answer 2

`color(blue)(n=10/9`

Explanation:

I'd like to answer this question (but was asked by me and then I found the answer)

Let the number be `n`

Then,

`color(orange)("Its reciprocal"=1/n`

`color(orange)("Its square"=n^2`

Let's put everything according to the question

`rarrnxxn^2xx1/n=100/81`

`rarrcancelnxxn^2xx1/canceln=100/81`

`rarrn^2=100/81`

Take the square root of both sides

`rarrsqrt(n^2)=sqrt(100/81)`

`rarrn=sqrt100/sqrt81`

`color(blue)(rArrn=10/9`