SAT math page 684 #16

Let *x* (very wierd if you ask me) be defined as *x* = x^2-x for all values of x. If *a*=*a-2*, what is the value of a?

a)1
b)1/2
c)3/2
d)6/5
e)3

I got this: (a-2)^2-(a-2) = a^2-3a+6. But the answer I got for a isn't in the choices. Any tips? Thanks in advance

I'm not sure what this problem is asking. Is it asking where does "x" and "a" intersect or what is x(a)? Is "*" a symbol in the book that is suppose to represent some type of operation like those problems with squares and triangles that you are suppose to figure out?

Lastly, from your wording of this problem it doesn't look like "x" is related with "a" in any shape or form.

Quote:

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Originally Posted by Linnus

I'm not sure what this problem is asking. Is it asking where does "x" and "a" intersect or what is x(a)? Is "*" a symbol in the book that is suppose to represent some type of operation like those problems with squares and triangles that you are suppose to figure out?

Lastly, from your wording of this problem it doesn't look like "x" is related with "a" in any shape or form.

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"*" IS a symbol in the book that is suppose to represent some type of operation like those problems with squares and triangles that you are suppose to figure out

Yeah i know, I don't think x and a are related at all. This is why I'm confused by this question.

Oh if * is an operation then

if *x*= x^2-x
and
*a*= *a-2*
then
a^2-a=(a-2)^2-(a-2)

Solve for a.

Quote:

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Originally Posted by fabxx

Let *x* (very wierd if you ask me) be defined as *x* = x^2-x for all values of x. If *a*=*a-2*, what is the value of a?

a)1
b)1/2
c)3/2
d)6/5
e)3

I got this: (a-2)^2-(a-2) = a^2-3a+6. But the answer I got for a isn't in the choices. Any tips? Thanks in advance

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You only have to use the given definition twice:

*a* = a² - a and

*a-2* = (a-2)² - (a-2)

That means you have to solve the equation:

a² - a = (a-2)² - (a-2)

I've got a = 3