Đáp án:
$x = 10 ; y = 10$
Giải thích các bước giải:
$\frac{x}{y} = \frac{y}{10} = \frac{10}{x}$
⇔ $10x = y^{2} ; xy = 100$
⇔ $x = \frac{y^{2}}{10} ; xy = 100$
⇒ $\frac{y^{2}}{10}×y = 100$
⇔ $y^{3} = 1000$
⇔ $y^{3} = 10^{3}$
⇔ $y = 10$
⇒ $x = \frac{10^{2}}{10}$
⇔ $x = 10$
Ta có :
`+` `x/y` = `y/10`
`=> x . 10 = y . y`
`=> 10x = y²`
`=> x =` `(y²)/10`
`+` `y/10` = `10/x`
`=> x . y = 10 . 10`
`=> xy = 100`
Thay `x =` `(y²)/10` vào `xy = 100` , ta có :
`(y²)/10` `. y = 100`
` ( y² . y )/10` `= 100`
`=> y³ = 100 . 10`
`=> y³ = 1000`
`=> y³ = 10³`
`=> y = 10`
Mà xy = 100
`=> x = 10`
Vậy `x = y = 10`
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