1986 年

If $r=\sqrt[3]{h^3-7r^3}$, then the ratio $r:h$ is

$\dfrac{\dfrac{x^2}{3}-3y^2}{\dfrac{3}{2}(x-3y)}=$

If $1-\dfrac{x+y}{y-x}=a$ ($a\ne0$), then $y=$

Which of the following is an identity/are identities? I. $(x+1)(x-1)=x^2+1$, II. $x^2-2x+1=0$, III. $(x-2)^2=(2-x)^2$.

Given the identity $\dfrac{2}{x-1}+\dfrac{x+1}{(x-1)^2}+\dfrac{a}{(1-x)^2}=\dfrac{bx-2}{(x-1)^2}$, find the values of the constants $a$ and $b$.

If $\alpha$ and $\beta$ are the roots of the equation $2x^2+x+3=0$, find the value of $\alpha-\dfrac{\alpha^2}{\alpha+\beta}$.

The figure shows an infinite number of squares. The length of a side of the first square is $1$. The side of the first square is equal to half of the side of the preceding one. Find the sum of the areas of the infinite number of squares.

Find the real value of $x$ such that $\begin{cases}x^2+x+1=k\\ x-1=\dfrac{7}{k}\end{cases}$, where $k$ is a constant.

The figure shows two sectors with radii $r$ and $2r$. If these two sectors are equal in area, then $\theta_1:\theta_2=$

In the figure, $ABCD$ is a straight line with $AB=BC=CD$. Three circles I, II and III are drawn respectively on $AB$, $AC$ and $AD$ as diameters. Areas of circle I : Area of circle II : Area of circle III $=$