France
Let ^@x^@ be a real number. What is the minimum value of ^@x^2 - 4x + 3^@?
Answer:
^@-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.
- 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} ^@ - 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^@. - Hence, the minimum value of ^@x^2 - 4x + 3^@ is ^@-1^@.
