SOLUTION: Suppose a and b are rational numbers. If the solutions to ax^2+2bx-a=0 are not rational, then show that the solutions to bx^2+2ax-b=0 are not rational.

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Question 31689: Suppose a and b are rational numbers. If the solutions to ax^2+2bx-a=0 are not rational, then show that the solutions to bx^2+2ax-b=0 are not rational.
Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!
Suppose a and b are rational numbers. If the solutions to ax^2+2bx-a=0 are not rational,
SO DISCRIMINANT = (2B)^2-4*(A)(-A)=4B^2+4A^2 IS NOT A PERFECT SQUARE........................I
then show that the solutions to bx^2+2ax-b=0 are not rational.
DISCRIMINANT =(2A)^2-4(B)(-B)= 4A^2+4B^2=4B^2+4A^2..........THIS IS NOT A PERFECT SQUARE AS PER I.HENCE THE ROOTS OF THIS QUADRATIC ARE ALSO IRRAIONAL
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