Question

Qual valor de x e de y?

Answer 1

faça a=√x →x=a²

e b=√y→ y=b²

{(a²)²+(b²)²=17

{a+b=3

{a⁴+b⁴=17

{a+b=3 →b=3-a

a⁴+(3-a)⁴=17

a⁴+81-108a+54a²-12a³+a⁴-17=0

2a⁴-12a³+54a²-108a+81-17=0

2a⁴-12a³+54a²-108a+64=0 ÷(2)

a⁴-6a³+27a²-54a+32=0

a⁴-4a³-2a³+19a²+8a²-16a-38a+32=0

a⁴-2a³-4a³+8a²+19a²-38a-16a+32=0

a³(a-2)-4a²(a-2)+19a(a-2)-16(a-2)=0

(a-2)(a³-4a²+19a-16)=0

a-2=0

a=2

b=3-a

b=3-2

b=1

x=a²=2²=4

y=b²=1²=1

S={4,1}