1994 年

If $\mathrm{f}(x)=x^2+2x$, then $\mathrm{f}(x-1)=$

If $y=\dfrac{2x-1}{x+2}$, then $x=$

The L.C.M. of $(x-1)^2$, $x^2-1$ and $x^3-1$ is

If $a=\sqrt3+\sqrt2$, then $a-\dfrac1a=$

In the figure, $(x,y)$ is a point in the shaded region (including the boundary) and $x$, $y$ are integers. Find the greatest value of $3x+y$.

If $x(x+1)<5(x+1)$, then

Which of the following is/are identity/identities?

I. $(x+2)(x-2)=x^2-4$ II. $(x+2)(x-2)=0$ III. $(x+2)^3=x^3+8$

If $\alpha\ne\beta$ and $\begin{cases} 3\alpha^2-h\alpha-b=0 \\ 3\beta^2-h\beta-b=0 \end{cases}$, then $\alpha+\beta=$

Mr. Chan bought a car for $\$143\,900$. If the value of the car goes down by $10\%$ each year, find its value at the end of the third year. (Give your answer correct to the nearest hundred dollars.)

A wholesaler sells an article to a retailer at a profit of $20\%$. The retailer sells it to a customer for $\$3\,600$ at a profit of $\$720$. Find the original cost of the article to the wholesaler.