Đáp án:
Giải thích các bước giải:
$\frac{x² + y²}{xy}$ = $\frac{5}{2}$
$\frac{x² + y² + 2xy - 2xy}{xy}$ = $\frac{5}{2}$
*TH1:
$\frac{(x + y)² - 2xy}{xy}$ = $\frac{5}{2}$
$\frac{(x + y)²}{xy}$ -2 = $\frac{5}{2}$
$\frac{(x + y)²}{xy}$ = 4,5 (1)
*TH2:
$\frac{(x - y)² + 2xy}{xy}$ = $\frac{5}{2}$
$\frac{(x-y)²}{xy}$ + 2 = $\frac{5}{2}$
$\frac{(x - y)²}{xy}$ =0,5 (2)
lấy $\frac{(1)}{(2)}$ :
$\frac{(x + y)²}{xy}$ : $\frac{(x - y)²}{xy}$ = $\frac{4,5}{0,5}$
$\frac{(x + y)²}{xy}$ . $\frac{xy}{(x - y)²}$ = 9
$\frac{(x + y)²}{(x - y)²}$ = 9
$\frac{x + y}{x - y}$ = ±3
