Question

admitere UPT 2019 AL 60​

Answer 1

Răspuns:

d

Explicație pas cu pas:

$\frac{1}{x} + \frac{1}{y} = 2\Big | \hat{}\,\,2\\\\\frac{1}{x^2} + \frac{1}{y^2} + 2\frac{1}{x}\frac{1}{y} = 4\\\\ 2 + 2\frac{1}{xy} = 4\\\\2\frac{1}{xy} = 2\\\\ \frac{1}{xy} = 1\\\\ xy=1\\\\ x = \frac{1}{y}\\\\ \frac{1}{x}+\frac{1}{y} = 2\\\\ \frac{1}{\frac{1}{y}} + \frac{1}{y} = 2\\\\ y + \frac{1}{y} = 2\Big | \cdot y\\\\ y^2 + 1 = 2y\\\\ y^2 - 2y + 1 = 0\\\\ (y-1)^2 = 0\\\\ y - 1 = 0\\\\ y = 1\\\\ x = \frac{1}{y} = \frac{1}{1} = 1$

Answer 2

Răspuns:

Explicație pas cu pas:

1/x+1/y=2          x+y=2xy       (x+y)²=4x²y²        x²+y²+2xy=4x²y²

1/x²+1/y²=2         (x²+y²)/x²y²=2        x²+y²=2x²y²

Scadem ecuatiile :        2xy=2x²y² ⇒1=xy       x=1/y

1/x+1/x=2      2/x=2         x=1    ⇒y=1    Rasp:   d