exactly equal

**futureprof** · September 7th 2009, 04:06 AM

Hi everyone

I am new here looking for a bit of help. Hopefully in the future I will be able to offer others some help.

I have been brushing up on my maths skills as I am starting a Home study maths degree. I have come accross the following question, and although I have trawled through many books, I can get nowhere with it.

X^2-aX+144=(x-b)^2

Find a and b.

Looks like something to do with a quadratic to me but I am totally stuck on how to get to the answer.

Any help would be greatly appreciated. Thanks.

James

**mr fantastic** · September 7th 2009, 04:10 AM

Originally Posted by futureprof

Hi everyone

I am new here looking for a bit of help. Hopefully in the future I will be able to offer others some help.

I have been brushing up on my maths skills as I am starting a Home study maths degree. I have come accross the following question, and although I have trawled through many books, I can get nowhere with it.

X^2-aX+144=(x-b)^2

Find a and b.

Looks like something to do with a quadratic to me but I am totally stuck on how to get to the answer.

Any help would be greatly appreciated. Thanks.

James

$(x - b)^2 = (x - b) (x - b) = x^2 - 2bx + b^2$ .

Compare this with $x^2 - ax + 144$ :

$-2b = -a \Rightarrow 2b = a$ .... (1)

$b^2 = 144 \Rightarrow b = \pm 12$ .... (2)

b = 12: a = 24.

b = -12: a = -24.

**futureprof** · September 7th 2009, 04:13 AM

Thanks for that.

So easy now I see it writen out.

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