`text{Đáp án:}`

\(\Leftrightarrow y=\pm\dfrac{41}{12}\)

`text{Giải thích các bước giải:}`

`x+`\(\left(\dfrac{-31}{12}\right)^2\)=\(\left(\dfrac{49}{12}\right)^2\)`-x=y`\(^{^{ }2}\)  

\(\Leftrightarrow x+\left(-\dfrac{31}{12}\right)^2=\left(\dfrac{49}{12}\right)^2-x\)    

\(\Leftrightarrow x+\left(-\dfrac{31}{12}\right)^2-\left(\dfrac{49}{12}\right)^2+x=0\)    

\(\Leftrightarrow2x+\left(-\dfrac{31}{12}\right)^2-\left(\dfrac{49}{12}\right)^2=0\)    

\(\Leftrightarrow2x+\dfrac{\left(-31\right)^2}{12^2}-\dfrac{49^2}{12^2}=0\)    

\(\Leftrightarrow2x+\dfrac{\left(-31\right)^2-49^2}{144}=0\)

\(\Leftrightarrow2x+\dfrac{961-2401}{144}=0\)

\(\Leftrightarrow2x+\dfrac{-1440}{144}=0\)

\(\Leftrightarrow2x+\left(-10\right)=0\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\)  

`Mà:` \(x+\left(-\dfrac{31}{12}\right)^2=y^2\)  

\(\Leftrightarrow5+\dfrac{961}{144}=y^2\)  

\(\Leftrightarrow y^2=\dfrac{1681}{144}\)

\(\Leftrightarrow y=\pm\dfrac{41}{12}\)

Đáp án:

Giải thích các bước giải:

`x + (-31)/12^2 = 49/12^2 - x = y^2`

Ta có: `x + (-31)/12^2 = 49/12^2 - x`

`<=> x + (-31)/144 = 49/144 - x`

`<=> x - 31/144 = 49/144 - x`

`<=> x - 31/144 + x = 49/144 `

`<=> 2x - 31/144 = 49/144 `

`<=> 2x = 49/144 + 31/144`

`<=> 2x = 88/144 = 5/9`

`<=> x = 5/18`

Mà: `49/12^2 - x = y^2`

`<=> y^2 = 49/12^2 - 5/18`

`<=> y^2 = 1/16`

`<=> y = \sqrt{1/16}`

`<=> y =±1/4`

Vậy `x = 5/18; y = ±1/4`