($x^{2}$ – 5)(x+3)=0 $\frac{x-12}{77}$ + $\frac{x-11}{78}$ = $\frac{x-74}{15}$ + $\frac{x-73}{16}$ 18/08/2021 Bởi Melody ($x^{2}$ – 5)(x+3)=0 $\frac{x-12}{77}$ + $\frac{x-11}{78}$ = $\frac{x-74}{15}$ + $\frac{x-73}{16}$
Giải thích các bước giải: `(x^2-5)(x+3)=0` `=>`\(\left[ \begin{array}{l}x^2-5=0\\x+3=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x^2=5\\x=-3\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=\pm\sqrt5\\x=-3\end{array} \right.\) `(x-12)/77+(x-11)/78=(x-74)/15+(x-73)/16` `=>((x-12)/77-1)+((x-11)/78-1)=((x-74)/15-1)+((x-73)/16-1)` `=>(x-89)/77+(x-89)/78=(x-89)/15+(x-89)/16` `=>(x-89)/77+(x-89)/78-(x-89)/15-(x-89)/16=0` `=>(x-89)(1/77+1/78-1/15-1/16)=0` Mà `1/77+1/78-1/15-1/16 ne 0` `=>x-89=0=>x=89` Bình luận
`(x^2-5)(x+3)=0` `<=>` \(\left[ \begin{array}{l}x^2-5=0\\x+3=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=\pm\sqrt{5}\\x=-3\end{array} \right.\) Vậy `S={\pm \sqrt{5}, -3}` `\frac{x-12}{77}+\frac{x-11}{78}=\frac{x-74}{15}+\frac{x-73}{16}` `=> \frac{x-12}{77}-1+\frac{x-11}{78}-1-(\frac{x-74}{15}-1+\frac{x-73}{16}-1)=0` `<=> \frac{x-12-77}{77}+\frac{x-11-78}{78}-\frac{x-74-15}{15}-\frac{x-73-16}{16}=0` `<=> (x-89)(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16})=0` Do `\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16} \ne 0` `=> x-89=0` `<=> x=89` Vậy `S={89}` Bình luận
Giải thích các bước giải:
`(x^2-5)(x+3)=0`
`=>`\(\left[ \begin{array}{l}x^2-5=0\\x+3=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x^2=5\\x=-3\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=\pm\sqrt5\\x=-3\end{array} \right.\)
`(x-12)/77+(x-11)/78=(x-74)/15+(x-73)/16`
`=>((x-12)/77-1)+((x-11)/78-1)=((x-74)/15-1)+((x-73)/16-1)`
`=>(x-89)/77+(x-89)/78=(x-89)/15+(x-89)/16`
`=>(x-89)/77+(x-89)/78-(x-89)/15-(x-89)/16=0`
`=>(x-89)(1/77+1/78-1/15-1/16)=0`
Mà `1/77+1/78-1/15-1/16 ne 0`
`=>x-89=0=>x=89`
`(x^2-5)(x+3)=0`
`<=>` \(\left[ \begin{array}{l}x^2-5=0\\x+3=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=\pm\sqrt{5}\\x=-3\end{array} \right.\)
Vậy `S={\pm \sqrt{5}, -3}`
`\frac{x-12}{77}+\frac{x-11}{78}=\frac{x-74}{15}+\frac{x-73}{16}`
`=> \frac{x-12}{77}-1+\frac{x-11}{78}-1-(\frac{x-74}{15}-1+\frac{x-73}{16}-1)=0`
`<=> \frac{x-12-77}{77}+\frac{x-11-78}{78}-\frac{x-74-15}{15}-\frac{x-73-16}{16}=0`
`<=> (x-89)(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16})=0`
Do `\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16} \ne 0`
`=> x-89=0`
`<=> x=89`
Vậy `S={89}`