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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?

Respuesta :

obasola1

Answer:

[tex]\sqrt{2-x}[/tex]  is the final answer

Step-by-step 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

[tex]\sqrt{x^2-6x+9} +\sqrt{2-x} +x-3[/tex]

[tex]\sqrt{x^2-6x+9} +\sqrt{2-x} +x-3[/tex] factorizing x^2-6x+9

[tex]\sqrt{(x-3)^2} +\sqrt{2-x} +x-3[/tex]..................1

take note that[tex]\sqrt{x^2} =IxI      modulus of x[/tex]

Ix-3I+[tex]\sqrt{2-x}[/tex]...................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)+[tex]\sqrt{2-x}[/tex]+x-3

[tex]\sqrt{2-x}[/tex]  is the final answer