# 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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