在 $\big(1+\tfrac{2}{p}x\big)^5+(1+px)^6$ 的展开式中，$x^2$ 的系数为 70。

求常数 $p$ 的可能值。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

分别找两个二次项的系数，再令 $u=p^2$，把所得方程化成关于 $u$ 的二次方程。

The coefficients are $\binom52(2/p)^2=40/p^2$ and $\binom62p^2=15p^2$. Their sum is $70$, with $p\ne0$. Multiplying by $p^2$ and dividing by $5$ gives $3p^4-14p^2+8=0$. For $u=p^2$,

The two values of $u$ are positive, giving $p=\pm\sqrt{2/3}$ or $p=\pm2$.