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Solve the equations: x + y = z x - 2 = y x^2 + y^2 = 8

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xataexa | Student, Kindergarten | Salutatorian

Posted April 19, 2011 at 2:38 PM via web

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Solve the equations:

x + y = z

x - 2 = y

x^2 + y^2 = 8

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1 Answer | Add Yours

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 19, 2011 at 3:17 PM (Answer #1)

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We have to solve the system of equations:

x + y = z ...(1)

x - 2 = y ...(2)

x^2 + y^2 = 8 ...(3)

From (2) we get y = x - 2

substitute in (3)

x^2 + (x - 2)^2 = 8

=> x^2 + x^2 + 4 - 4x = 8

=> 2x^2 - 4x - 4 = 0

=> x^2 - 2x - 2 = 0

x1 = 2/2 + sqrt (4 + 8) / 2

=> 1 + sqrt 3

x2 = 1 - sqrt 3

y1 = sqrt 3 - 1

y2 = -sqrt 3 - 1

z1 = 2*sqrt 3

z2 = -2*sqrt 3

The solution of the equations are: (1 + sqrt 3 , sqrt 3 - 1 , 2*sqrt 3) and (1 - sqrt 3 , -sqrt 3 - 1 , -2*sqrt 3)

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