( 4x - 5 )( 5/4x - 2 ) = 1 1/3

Đáp án: $x=\dfrac{171}{120}\pm\sqrt{\dfrac{3667}{4800}}$

Giải thích các bước giải:

Ta có:

$(4x-5)(\dfrac54x-2)=\dfrac{11}3$

$\to 5x^2-\dfrac{57}4x+10=\dfrac{11}3$

$\to 60x^2-171x+120=44$

$\to 60x^2-171x+76=0$

$\to x^2-\dfrac{171}{60}x+\dfrac{19}{15}=0$

$\to x^2-2x\cdot \dfrac{171}{120}+(\dfrac{171}{120})^2+\dfrac{19}{15}-(\dfrac{171}{120})^2=0$

$\to (x-\dfrac{171}{120})^2-\dfrac{3667}{4800}=0$

$\to (x-\dfrac{171}{120})^2=\dfrac{3667}{4800}$

$\to x-\dfrac{171}{120}=\pm\sqrt{\dfrac{3667}{4800}}$

$\to x=\dfrac{171}{120}\pm\sqrt{\dfrac{3667}{4800}}$