This is a new problem as asked by a anonymous visitor which read: "a number added to five times its reciprocal is -6. find the number "

Ok non-algebraically you can think of what numbers added together will make 6(of course they will be negative to make negative 6) --- 1 and 5 and 4 and 2 , and 6 and 0... You can't have a reciprocal of 0 and a reciprocal of 6 : 1/6 when multiplied by 5 makes 5/6ths and you know those added together : -6 + - 5/6ths dont make -6. Same thing goes for 2 and 3 --> 2 + 5/2 or 3 + 5/3 dont make 6. 1 and 5 however do work. The reciprocal of 1 is 1 so 1 + 5/1 =6 and so does 5 + 5/5 = 6 (Of course negative again). So there are 2 answers -1 and -5...

Algebraically... -x + (1/-x)5 = -6 =

-x -5/x = -6 (multiply by -x)

x^2 + 5 = 6x

x^2 + 6x + 5 = 0

(x + 1) (x + 5 ) = 0

So the answers are x = -1 and -5

## Friday, October 7, 2011

### Number Problem 11 Solution

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a number added to five times its reciprocal is = to -6

ReplyDeletehence let x be the number

and 5x be the five times

x + 5x = -6

6x = -6

-6 / 6

= -1

-1 times 5 = -5

-1 + -5 = -6