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

Toán Lớp 11: Sin2x + 4(Sinx + Cosx) – 6 = 0

Tháng Một 7, 2023 Toán học 1 Comment 0 views

Toán Lớp 11: Sin2x + 4(Sinx + Cosx) – 6 = 0

Comments ( 1 )

  1. huongtructram
    huongtructram
    7 Tháng Một, 2023 at 11:02 sáng
    Reply
    Đặt $t=\sin x+\cos x$ ($t\in [-\sqrt2;\sqrt2]$)
    $\to \sin2x=t^2-1$
    PT trở thành:
    $t^2-1+4t-6=0$
    $\to t^2+4t-7=0$
    $\to t=-2+\sqrt{11}$ do $t\in [-\sqrt2;\sqrt2]$
    $\to \sqrt2\sin\left(x+\dfrac{\pi}{4}\right)=-2+\sqrt{11}$
    $\to \sin\left(x+\dfrac{\pi}{4}\right)=\dfrac{-2+\sqrt{11}}{\sqrt2}=\dfrac{\sqrt{22}-2\sqrt2}{2}$
    $\to \left[ \begin{array}{l}x=\dfrac{-\pi}{4}+\arcsin\dfrac{\sqrt{22}-2\sqrt2}{2}+k2\pi \\x=\dfrac{3\pi}{4}-\arcsin\dfrac{\sqrt{22}-2\sqrt2}{2}+k2\pi \end{array} \right.$

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

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