Question

(3 x - 5 ) . ( 4x - 7 ) = 1

Answer 1

\(\left(3x-5\right)\left(4x-7\right)=1\)

\(\Rightarrow12x^2-41x+34=0\)

\(\Rightarrow12x\left(x-2\right)-17\left(x-2\right)=0\)

\(\Rightarrow\left(x-2\right)\left(12x-17\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{17}{12}\end{matrix}\right.\)

Answer 2

(3x - 5)(4x - 7) = 1

<=> 12x² - 21x - 20x + 35 = 1

<=> 12x² - 41x + 34 = 0

<=> 12x² - 24x - 17x + 34 = 0

<=> 12x(x - 2) - 17(x - 2) = 0

<=> (12x - 17)(x - 2) = 0

<=> \(\left[{}\begin{matrix}12x-17=0\\x-2=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{17}{12}\\x=2\end{matrix}\right.\)

Answer 3

\(\Leftrightarrow12x^2-41x+35-1=0\)

\(\Leftrightarrow12x^2-41x+34=0\)

\(\text{Δ}=\left(-41\right)^2-4\cdot12\cdot34=49\)

Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{41-7}{24}=\dfrac{17}{12}\\x_2=\dfrac{41+7}{24}=2\end{matrix}\right.\)

Answer 4

(3x-5).(4x-7)=1

=> 3x-5=1 hoặc 4x-7=1

-> 3x-5=1

    3x   =1+5

    3x   = 6

      x   = 6:3

      x   = 2

-> 4x-7=1

    4x   =1+7

    4x   = 8

       x   = 8: 4

       x   = 2

Vậy x = .....tự ghi nốt