Question

Se dă sistemul: x+y=3
xy=-10
Rezultatul calcului x^2+y^2????

Answer 1

y=3-x
x(3-x)=-10

y=3-x
3x-x²=-10

y=3-x
-x²-3x+10=0

Rezolvam ecuatia de gr. Il
-x²-3x+10=0
D=b²-4ac=(-3)²-4•(-1)•10=9+40=49=7²>0
x1=(-b-√D)/2a=( -(-3)-√7²)/2•(-1)=(3-7)/-2=-4/-2=2
x2=(-b-√D)/2a=( -(-3)+√7²)/2•(-1)=(3+7)/-2=10/-2=-5

y1=3-2=1
y2=3+5=8

x1²+y1²=2²+1²=5
x2²+y2²=(-5)²-8²=25+64=89