Toán Lớp 8: Tìm x (x—5)(x+5)+3(3—x)=—11+10x

Toán Lớp 8: Tìm x
(x—5)(x+5)+3(3—x)=—11+10x

TRẢ LỜI

  1. $\text{(x – 5)(x + 5) + 3(3 – x) = -11 + 10x}$
    $\text{⇔ (x² – 25) + (9 – 3x) – (-11 + 10x) = 0}$
    $\text{⇔ x² – 25 + 9 – 3x + 11 – 10x = 0}$
    $\text{⇔ x² – 13x – 5 = 0}$
    $\text{⇔ (x² – 13x) – 5 = 0}$
    $\text{⇔ [(x)² – 2.x.$\dfrac{13}{2}$ + ($\dfrac{13}{2}$)² – ($\dfrac{13}{2}$)²] – 5 = 0}$
    $\text{⇔ (x – $\dfrac{13}{2}$)² – $\dfrac{169}{4}$ – 5 = 0}$
    $\text{⇔ (x – $\dfrac{13}{2}$)² – $\dfrac{189}{4}$ = 0}$
    $\text{⇔ (x – $\dfrac{13}{2}$)² = $\dfrac{189}{4}$}$
    $\text{⇔ (x – $\dfrac{13}{2}$)² = (±$\dfrac{3\sqrt{21}}{2}$)²}$
    $\text{⇒ x – $\dfrac{13}{2}$ = ±$\dfrac{3\sqrt{21}}{2}$}$
    $\text{⇔ $\left[\begin{matrix} x – \dfrac{13}{2} = \dfrac{3\sqrt{21}}{2}\\x – \dfrac{13}{2} = – \dfrac{3\sqrt{21}}{2}\end{matrix}\right.$}$
    $\text{⇔ $\left[\begin{matrix} x = \dfrac{13 + 3\sqrt{21}}{2} \\ x = \dfrac{13 – 3\sqrt{21}}{2} \end{matrix}\right.$}$
    $\text{Vậy x ∈ {$\dfrac{13 ± 3\sqrt{21}}{2}$}}$
    $\textit{Ha1zzz}$
     

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