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Question: Erroneous FALSE return on quadratic expression?

Question:Erroneous FALSE return on quadratic expression?

tsunamiBTP 292 Maple 12
false quadratic
June 20 2012
0

See attached.  I have stared at this long enough to the point I need some FRESH eyes on this.  Why does MAPLE return FALSE on the last 2 statements

a := MAG^2-1; 1; b := 2*tan(FAZE)*(2*tau*Omega+Omega^2*beta*tau^2-beta); 1; c := -(beta^2+1)*(1+Omega^2*tau^2)^2*tan(FAZE)^2

-(beta^2+1)*(1+Omega^2*tau^2)^2*tan(FAZE)^2

 (1)

b^2-4*a*c = (2*tan(FAZE)*(2*tau*Omega+Omega^2*beta*tau^2-beta))^2+(4*(MAG^2-1))*(beta^2+1)*(1+Omega^2*tau^2)^2*tan(FAZE)^2
(->)true(->)true(->)true(->)false(->)true

b^2-4*a*c = 4*tan(FAZE)^2*((2*tau*Omega+Omega^2*beta*tau^2-beta)^2+(MAG^2-1)*(beta^2+1)*(1+Omega^2*tau^2)^2)
(->)true(->)true(->)true(->)true

(2*tau*Omega+Omega^2*beta*tau^2-beta)^2-(beta^2+1)*(1+Omega^2*tau^2)^2(=)-(-1+Omega^2*tau^2-2*beta*Omega*tau)^2

b^2-4*a*c = 4*tan(FAZE)^2*(MAG^2*(beta^2+1)*(1+Omega^2*tau^2)^2-(Omega^2*tau^2-2*beta*Omega*tau-1)^2)(->)true(->)true

-`&+-`(b, sqrt(b^2-4*a*c))/(2*a) = (-2*tan(FAZE)*`&+-`(2*tau*Omega+Omega^2*beta*tau^2-beta, sqrt(4*tan(FAZE)^2*(MAG^2*(beta^2+1)*(1+Omega^2*tau^2)^2-(Omega^2*tau^2-2*beta*Omega*tau-1)^2))))*(1/(2*(MAG^2-1)))
(->)false(->)false(->)false

`&+-`(sqrt(b^2-4*a*c)) = `&+-`(sqrt(4*tan(FAZE)^2*(MAG^2*(beta^2+1)*(1+Omega^2*tau^2)^2-(Omega^2*tau^2-2*beta*Omega*tau-1)^2)))
(->)true

-b = -2*tan(FAZE)*(2*tau*Omega+Omega^2*beta*tau^2-beta)(->)true

-b+`&+-`(sqrt(b^2-4*a*c)) = -2*tan(FAZE)*(2*tau*Omega+Omega^2*beta*tau^2-beta)+`&+-`(sqrt(4*tan(FAZE)^2*(MAG^2*(beta^2+1)*(1+Omega^2*tau^2)^2-(Omega^2*tau^2-2*beta*Omega*tau-1)^2)))
(->)true(->)true(->)false

-`&+-`(b, sqrt(b^2-4*a*c))/(2*a) = (-2*tan(FAZE)*`&+-`(2*tau*Omega+Omega^2*beta*tau^2-beta, sqrt(4*tan(FAZE)^2*(MAG^2*(beta^2+1)*(1+Omega^2*tau^2)^2-(Omega^2*tau^2-2*beta*Omega*tau-1)^2))))*(1/(2*(MAG^2-1)))
(->)false

-`&+-`(b, sqrt(b^2-4*a*c))/(2*a)

-(1/2)*`&+-`(2*tan(FAZE)*(2*tau*Omega+Omega^2*beta*tau^2-beta), 2*(tan(FAZE)^2*(2*tau*Omega+Omega^2*beta*tau^2-beta)^2+(MAG^2-1)*(beta^2+1)*(1+Omega^2*tau^2)^2*tan(FAZE)^2)^(1/2))/(MAG^2-1)

 (2)

-`&+-`(b, sqrt(b^2-4*a*c))/(2*a) = -1/2*(2*tan(FAZE)*`&+-`(2*tau*Omega+Omega^2*beta*tau^2-beta, 2)*sqrt(tan(FAZE)^2*(2*tau*Omega+Omega^2*beta*tau^2-beta)^2+(MAG^2-1)*(beta^2+1)*(1+Omega^2*tau^2)^2*tan(FAZE)^2)/(MAG^2-1))
(->)false``

``

 

Download quadratic_formula_fa.mw

when the previous statements return TRUE?
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