Question

Help with signs, The sum of two numbers is 8, and their product is 9, 75, what are they?

So, the answer in the book states: 1, 5 and 6, 5.

But when I do the Algebra, I get:

`x + y = 8` ; `x*y = 9, 75`

x = 8 - y

9, 75 = (8 - y ) y

`y^2 -8y - 9, 75`

And then quadratic formula:

`(- b +- sqrt(b^2 - 4ac)) /2`

Which gives:

`(- b +- sqrt(64 - 4(-9, 75)(1) )) /2`

`(- b +- sqrt(64 +39)) /2`

`(- b +- sqrt(103)) /2`

The way to get 1, 5 and 6, 5 would be to have 64 - 39 in the parrnethesis, but I always get a cancelation of signs, either with - y^2 or -9, 5.

Help please.

Answer 1

`1.5` and `6.5`

Explanation:

You have the problem essentially worked out so:
`x+y=8`
`xy=9.75`

Substitute for `x`
`x=-y+8`
`(-y+8)y= 9.75`

This is where there was a minor error, `-y*y` is `-y^2`

`-y^2+8y-9.75=0`

`y=(-8+-sqrt(64-4(-1)(-9.75)))/(2(-1))`

`y=(-8+-sqrt(25))/(-2)`

`y= 4+-5/2`

`y= 6.5 or 1.5`

So you can decide which number you want for `x` and which you want for `y`:

The numbers are:
`1.5` and `6.5`