Giải phương trình sau x-85/15+x-74/13+x-67/11+x-64/9=10 Giúp với ạ mình đang cần gấp 18/07/2021 Bởi Eloise Giải phương trình sau x-85/15+x-74/13+x-67/11+x-64/9=10 Giúp với ạ mình đang cần gấp
$\dfrac{x-85}{15}+\dfrac{x-74}{13}+\dfrac{x-67}{11}+\dfrac{x-64}{9}=10$ `<=>` $\left({\dfrac{x-85}{15}-1}\right)+\left({\dfrac{x-74}{13}-2}\right)+\left({\dfrac{x-67}{11}-3}\right)+\left({\dfrac{x-64}{9}-4}\right)=0$ `<=>` $\dfrac{x-100}{15}+\dfrac{x-100}{13}+\dfrac{x-100}{11}+\dfrac{x-100}{9}=0$ `<=>` $(x-100).\left({\dfrac{1}{15}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}}\right)=0$ `<=>` $x-100=0.$ (Vì $\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}\neq0$) `<=>`$x=100$ Bình luận
Đáp án: 100 Giải thích các bước giải: $\frac{x-85}{15}$+ $\frac{x-74}{13}$+ $\frac{x-67}{11}$+ $\frac{x-64}{9}$=10 ⇔ ($\frac{x-85}{15}-1$ ) + ($\frac{x-74}{13}-2$ ) + ($\frac{x-67}{11}-3$ ) + ($\frac{x-64}{9}-4$ ) = 0 ⇔ $\frac{x-100}{15}$ + $\frac{x-100}{13}$ + $\frac{x-100}{11}$ + $\frac{x-100}{9}$ = 0 ⇔ (x-100).($\frac{1}{15}$ + $\frac{1}{13}$ +$\frac{1}{11}$ + $\frac{1}{9}$) = 0 ⇔ x-100 = 0 ⇔ x = 100 Bình luận
$\dfrac{x-85}{15}+\dfrac{x-74}{13}+\dfrac{x-67}{11}+\dfrac{x-64}{9}=10$
`<=>` $\left({\dfrac{x-85}{15}-1}\right)+\left({\dfrac{x-74}{13}-2}\right)+\left({\dfrac{x-67}{11}-3}\right)+\left({\dfrac{x-64}{9}-4}\right)=0$
`<=>` $\dfrac{x-100}{15}+\dfrac{x-100}{13}+\dfrac{x-100}{11}+\dfrac{x-100}{9}=0$
`<=>` $(x-100).\left({\dfrac{1}{15}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}}\right)=0$
`<=>` $x-100=0.$ (Vì $\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}\neq0$)
`<=>`$x=100$
Đáp án:
100
Giải thích các bước giải:
$\frac{x-85}{15}$+ $\frac{x-74}{13}$+ $\frac{x-67}{11}$+ $\frac{x-64}{9}$=10
⇔ ($\frac{x-85}{15}-1$ ) + ($\frac{x-74}{13}-2$ ) + ($\frac{x-67}{11}-3$ ) + ($\frac{x-64}{9}-4$ ) = 0
⇔ $\frac{x-100}{15}$ + $\frac{x-100}{13}$ + $\frac{x-100}{11}$ + $\frac{x-100}{9}$ = 0
⇔ (x-100).($\frac{1}{15}$ + $\frac{1}{13}$ +$\frac{1}{11}$ + $\frac{1}{9}$) = 0
⇔ x-100 = 0
⇔ x = 100