Toán Lớp 9: Giải pt: `-6t^2-5t-10=0` Chi tiết nka.

Question

Toán Lớp 9:  Giải pt: -6t^2-5t-10=0 Chi tiết nka.

aivilanlan · Answer

Giải đáp:     $ begin{array}{l}6t^2-5t-10=0   leftrightarrow 6t^2-5t=10   leftrightarrow t^2- dfrac{5}{6}t= dfrac{5}{3}   leftrightarrow t^2- dfrac{5}{6}x+ dfrac{25}{144}= dfrac{5}{3}+ dfrac{25}{144}   leftrightarrow  left({t- dfrac{5}{12}} right)^2= dfrac{265}{144}   leftrightarrow t- dfrac{5}{12}= pm dfrac{ sqrt{265}}{12}   leftrightarrow  left[ begin{array}{l}t- dfrac{5}{12}=- dfrac{ sqrt{265}}{12}  t- dfrac{5}{12}= dfrac{ sqrt{265}}{12} end{array} right.   leftrightarrow  left[ begin{array}{l}t= dfrac{- sqrt{265}+5}{12}  t= dfrac{ sqrt{265}+5}{12} end{array} right.   text{Vậy}   S= left {{ dfrac{- sqrt{265}+5}{12}; dfrac{ sqrt{265}+5}{12}} right } end{array}$

hienchaudiem · Answer

6t^2-5t-10=0 <=>t^2-5/6t-5/3=0 <=>(t-5/12)^2-265/144=0 <=>(t-5/12- frac{ sqrt{265}}{12})(t-5/12+ frac{ sqrt{265}}{12})=0 <=> ( left[ begin{array}{l}t- dfrac{5}{12}- dfrac{ sqrt{265}}{12}=0 t- dfrac{5}{12}+ dfrac{ sqrt{265}}{12}=0 end{array} right. ) <=> ( left[ begin{array}{l}t= dfrac{ sqrt{265}+5}{12} t=- dfrac{ sqrt{265}+5}{12} end{array} right. ) Vậy S={ frac{ sqrt{265}+5}{12};- frac{ sqrt{265}+5}{12}}