Question

If each expression under the square root is greater than or equal to 0, what is x2−6x+9−−−−−−−−−√+2−x−−−−√+x−3x2−6x+9+2−x+x−3?

Answer 1

`√(2-x)` is the final answer

Explanation:

If each expression under the square root is greater than or equal to 0, what is x2−6x+9−−−−−−−−−√+2−x−−−−√+x−3x2−6x+9+2−x+x−3?

can be rearranged as thus

`√(x^2-6x+9) +√(2-x) +x-3`

`√(x^2-6x+9) +√(2-x) +x-3` factorizing x^2-6x+9

`√((x-3)^2) +√(2-x) +x-3`..................1

take note that
`√(x^2) =IxI      modulus of x`

Ix-3I+
`√(2-x)`...................2

Ix-3I is equal to -(x-3)...............3

Now, as the expressions under the square roots are greater than or equal to zero than 2−x≥0

2−x≥0

--> -x≤-2

x≤2.

substituting 3 into the equation 2

-(x-3)+
`√(2-x)`+x-3

`√(2-x)` is the final answer