Let ^@x^@ be a real number. What is the minimum value of ^@x^2 - 4x + 3^@?


Answer:

^@-1^@

Step by Step Explanation:
  1. We are given a quadratic equation ^@x^2 - 4x + 3^@, where x is a real number and we need to find the minimum value of this equation.
  2. Now, we have,
    ^@ \begin{align} x^2 - 4x + 3 & = x^2 - 4x + 4 - 1 \\ & = x^2 - 2(2)x + 2^2 - 1 \\ & = (x - 2)^2 - 1 \end{align} ^@
  3. Observe that the value of ^@x^2 - 4x + 3^@ will be minimum when ^@(x - 2)^2 = 0, i.e. \space x = 2^@
    The value of ^@x^2 - 4x + 3^@ at ^@x = 2^@ is ^@-1^@.
  4. Hence, the minimum value of ^@x^2 - 4x + 3^@ is ^@-1^@.

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