Question

Daca x+y=4
         xy=3
a) x^2+y^2=?
b) (x-y)^2=?
c)1/x+1/y=?
 
Repede 20 pcte!!

Answer 1

a) (x+y)(x+y)=x²+xy+xy+y²
(x+y)(x+y)-xy-xy=x²+y²
4*4-3-3=10

b) (x-y)²=x²-2xy+y²=x²+y²-2xy=10-2*3=4

c) $\frac{1}{x}+ \frac{1}{y}= \frac{x+y}{xy}= \frac{4}{3}$