Question

Se x+y= 5 e x.y= -12, então o valor da expressão x²+y² é?

Answer 1

Resposta:

x+y=5

xy = -12

x = 5 - y

(5-y)y = -12

-y² + 5y = -12

-y² + 5y +12 = 0

x = -(5)±√(5)²-4(-1)(12)

----------------------------------

2(-1)

x = -5 ± √25 + 48

-----------------------

-2

x = -5 ± √73

--------------

-2

x = 5 ± √73

------------

2

x = 5 - y

5+√73 2(5-y)

----------- = -----------

2 2

5 + √73 = 10 - 2y

-2y = 5 + √73 - 10

-2y = -5 + √73

Y = -5 + √73

---------------

-2

Y = 5 + √73

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2

x² + y²

(5 + √73)² (5+√73)²

------------ + --------------

2 2

25 + 10√73 + 73 25 + 10√73 + 73

---------------------------- + -----------------------------

4 4

50 + 20√73 + 146

-------------------------------

4

196 + 20√73

----------------------

4

98 + 10√73

--------------------

2

49 + 5√73