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CIE 9709 2025 June Paper 15 Q3

A Level / CIE / P1

CIE 9709 2025 June Paper 15 Paper · Question 3

题目

Problem

(a) Use completing the square to find the exact solutions of the equation 4x2−4x−1=04x^2-4x-1=0.

[2]

(b) Hence solve the equation 4tan⁡θ=4+1tan⁡θ4\tan\theta=4+\frac{1}{\tan\theta} for 0∘<θ<180∘0^\circ<\theta<180^\circ.

[3]
题目中文翻译

(a) 用配方法求方程 4x2−4x−1=04x^2-4x-1=0 的精确解。

(b) 由此解方程 4tan⁡θ=4+1tan⁡θ4\tan\theta=4+\frac{1}{\tan\theta}，其中 0∘<θ<180∘0^\circ<\theta<180^\circ。

解答