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

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Please help...Thanks!!!

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Answer 1 · 2016-10-31T14:27:13

The 10 divided by 9

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 · 2016-10-31T14:33:05

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

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#