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 ?
Answer 1.
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If each term in this expression is well defined.
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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)
Ans: 1
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)
Ans: 1
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Amiable Scholar
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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 =<2lenagmat 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 ?
=> 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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