Qual o valor das duas variáveis?
w²+z²=178
z*w=80
(w+z)²=w²+z²+2zw =178+2*80
(w+z)²=338 ==> w+z=±13√2 (i)
(w-z)²=w²+z²-2*wz=178-2*80=18
(w-z)²=18 ==>w-z=±3√2 (ii)
Se w+z=13√2 (i) e w-z=3√2 (ii)
(i)+(ii) ===> 2w=13√2+3√2 ==>w=8√2 e z =5√2
Se w+z=13√2 (i) e w-z=-3√2 (ii)
(i)+(ii) ===> 2w=13√2-3√2 ==>w=5√2 e z =8√2
Se w+z=-13√2 (i) e w-z=3√2 (ii)
(i)+(ii) ===> 2w=-13√2+3√2 ==>w=-5√2 e z =-8√2
Se w+z=-13√2 (i) e w-z=-3√2 (ii)
(i)+(ii) ===> 2w=-13√2-3√2 ==>w=-8√2 e z =-5√2
Quanto é (w-z)²?
(w-z)²=w²+z²-2*wz
=178-2*80
=18
