Question

Daca x+y=-√2 si xy= -12 , calculati :
a) x²+y²
b)x-y

Raspunsurile sunt :
a) 26
b)+-5√2 doar ca mie imi trebuie rezolvarea completa.

Answer 1

x+y=-√2 il poti ridica la a doua
x²+2xy+y²=2
x²+y²=2-2xy
x²+y²=2+24
x²+y²=26

Answer 2

a)
x+y=-√2
si xy= -12 
(x+y)²=(-√2 )²
x²+2xy+y²=2
x²+y²=2-2xy=2-2(-12)=2+24=26

b)
x²+y²=26
x²+y²-2xy=26-2(-12)=26+24=50
(x-y)²=50
x-y=√50     x-y=√2×5² ⇒   x-y=+5√2     x-y=-5√2