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If each term in this expression is well defined.

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If each term in this expression is well defined.

by lenagmat » Thu Oct 27, 2011 11:40 am
What is sqrt(x^2-6x+9)+sqrt(2-x)+(x-3) if each term in this expression is well defined ?

1. sqrt(2-x)
2. 2x-6+sqrt(2-x)
3. sqrt(2-x)+(x-3)
4. 2x-6+sqrt(x-2)
5. x+sqrt(x-2)

And just for the future - what does it mean - if each term in expression is well defined ?

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by GmatMathPro » Thu Oct 27, 2011 12:15 pm
They mean that the value of x is such that none of the expressions are imaginary or undefined. For example, √(2-x) is only a real number if 2-x>=0. That is, x<=2.

First, factor x^2-6x+9 as (x-3)^2. √(x-3)^2=|x-3|, but we know that x<=2, so |x-3|=3-x.

So, 3-x+√(2-x)+x-3=

√(2-x)

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by Amiable Scholar » Thu Oct 27, 2011 6:09 pm
lenagmat wrote:What is sqrt(x^2-6x+9)+sqrt(2-x)+(x-3) if each term in this expression is well defined ?

And just for the future - what does it mean - if each term in expression is well defined ?
It means the each term is a real term ... sqrt(x^2-6x+9) is real and also sqrt(2-x) is well defined here .. i.e. it a real number => 2-x>=0 =>x =<2

=> sqrt(x^2 -2.x.3 + 3.3) => sqrt( (x-3)^2) => |x-3| but x=<2 => |x-3|= 3-x


so the given expression get resolved to

3-x + sqrt(2-x) + x- 3
=sqrt(2-x)
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