`( x – 5 )( x – 6 )( x – 7 )( x – 8 ) + 1 = 829`

1 bình luận về “`( x – 5 )( x – 6 )( x – 7 )( x – 8 ) + 1 = 829`”

1. → Ta có :

   ( x – 5 )( x – 6 )( x – 7 )( x – 8 ) + 1 = 829

   ⇔ [ ( x – 5 )( x – 8 ) ][ ( x – 6 )( x – 7 ) ] + 1 = 829

   ⇔ ( x² – 13x + 40 )( x² – 13x + 42 ) + 1 = 829

   → Đặt  a = x² – 13x + 40  ta được :

   ⇔ a( a + 2 ) + 1 = 829

   ⇔ a² + 2a + 1 = 829

   ⇔ ( a + 1 )² – $\sqrt{829}$² =0

   ⇔ ( a + 1 + $\sqrt{829}$ )( a + 1 – $\sqrt{829}$ ) =0

   ⇔ $\left[\begin{matrix} a + 1 + \sqrt{829}=0\\a+1- \sqrt{829}=0\end{matrix}\right.$

   ⇔ $\left[\begin{matrix} a= -1- \sqrt{829}\\ a = -1 + \sqrt{829}\end{matrix}\right.$

   5 sao nha

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