Question

Resolva os sistemas seguintes
${x}^{2} + {y}^{2} = 17 \\ xy = 4$
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Answer 1

x²+y²=17

xy=4 ==> x=4/y

(x+y)²=x²+y²+2xy =17 +2*4= 17+8 =25

x+y=5

4/y+y=5

multiplique tudo por y

4+y²=5y

y²-5y+4=0

y'=[5+√(25-16)]/2=(5+3)/2=4     ==>x= 4/y=4/4=1

y''=[5-√(25-16)]/2=(5-3)/2=1   ==>x= 4/y=4/1=4

resposta ==> (1,4)  ,  (4,1)