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If ( 1 + sqrt 2 ) and ( 1 - sqrt 2 ) are the roots of equation ax^2 + bx - 1 = 0, then find the values of a and b.

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If ( 1 + sqrt 2 ) and ( 1 - sqrt 2 ) are the roots of equation ax^2 + bx - 1 = 0, then find the values of a and b.
posted Mar 31, 2016 by Rajni

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1 Answer

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We will solve the system of two equations as follows:
Let introduce the root values into the equation ax^2 + bx - 1= 0
a( 1+sqrt 2 )^2 + b ( 1 + sqrt 2) - 1 = 0
a( 1 - sqrt 2)^2 + b ( 1 - sqrt 2) - 1 = 0
Solving the system of two equations, yields : a = - b/ 2
Replacing the value of a into the first equation, yields: b = -2 Then a = 1
The cuadratic equation is x^2- 2x -1 = 0

answer Apr 2, 2016 by anonymous
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