Question

Se stie ca X+Y=4 , iar XY=3 , Calculati :
a) x² + y²
b) (x-y)²
c)$\frac{1}{x} + \frac{1}{y}$

Answer 1

rezolvare...........................

Answer 2

daca
a)...x+y=4 atunci (x+y)² = 4 ²  ⇒ x²+2xy+y²=16  ⇒ x²+y²+2*3=16  deci x²+y²=10 ;
b)...                     (x-y)² = x²-2xy+y² = x²+y² - 2 * xy = 10 - 2*3 = 4 ;
c)...                    1/x+1/y= (x+y) / xy = 4 / 3