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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: 2cos² ( x/2 + π/4 ) +√2 cos (x/2 + π/4 ) – 2 = 0

Home/ Toán Lớp 11: 2cos² ( x/2 + π/4 ) +√2 cos (x/2 + π/4 ) – 2 = 0

Toán Lớp 11: 2cos² ( x/2 + π/4 ) +√2 cos (x/2 + π/4 ) – 2 = 0

Tháng Tám 16, 2022 Toán học 1 Comment 0 views

Toán Lớp 11: 2cos² ( x/2 + π/4 ) +√2 cos (x/2 + π/4 ) – 2 = 0

Comments ( 1 )

  1. kimlien
    kimlien
    16 Tháng Tám, 2022 at 4:43 sáng
    Reply
    Đặt t=cos(\frac{x}{2}+\frac{π}{4}) \ (-1≤t≤1)
    Phương trình trở thành:
    2t^2+\sqrt{2}t-2=0
    ⇔ $\left [\begin{array}{l} t=\dfrac{\sqrt{2}}{2} & (Nhan) \\ t=-\sqrt{2} & (Loai) \end{array} \right.$
    Với t=\frac{\sqrt{2}}{2}:
    cos(\frac{x}{2}+\frac{π}{4})=\frac{\sqrt{2}}{2}
    ⇔ cos(\frac{x}{2}+\frac{π}{4})=cos\frac{π}{4}
    ⇔ $\left [\begin{array}{l} \dfrac{x}{2}+\dfrac{π}{4}=\dfrac{\pi}{4}+k2π \\ \dfrac{x}{2}+\dfrac{π}{4}=-\dfrac{\pi}{4}+k2π \end{array} \right.$
    ⇔ $\left [\begin{array}{l} \dfrac{x}{2}=k2π \\ \dfrac{x}{2}=-\dfrac{\pi}{2}+k2π \end{array} \right.$
    ⇔ $\left [\begin{array}{l} x=k4π \\ x=-\pi+k4π \end{array} \right. \ (k∈\mathbb{Z})$
    Vậy S={k4π, -π+k4π | k∈\mathbb{Z}}

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222-9+11+12:2*14+14 = ? ( )

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