Equation x^2

danielvnl

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Jan 3, 2013
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x2/3 - (28x)/3 + 9 = 0

(28/3 +- sqrt( (28/3)^2 -4(1/3)(9))/2(1/3)

I think there aren't naturals roots.
I tried on solve this equation but I can't.
When I paste it in Wolfram it gave me the result as 1 and 27.

Why ??
 
x2/3 - (28x)/3 + 9 = 0

(28/3 +- sqrt( (28/3)^2 -4(1/3)(9))/2(1/3)
When I paste it in Wolfram it gave me the result as 1 and 27.


Why don't you rewrite first as x228x+27=0 ?\displaystyle x^2-28x+27=0~?
 
As pka said, multiplying by 3 gives x228x+27=(x1)(x27)\displaystyle x^2- 28x+ 27= (x- 1)(x- 27)

But the quadratic formula certainly ought to give them too!

The "discriminant" is b24ac=(283)24(13)(9)=7849363=78491089\displaystyle b^2- 4ac= \left(\frac{28}{3}\right)^2- 4\left(\frac{1}{3}\right)(9)= \frac{784}{9}- \frac{36}{3}= \frac{784}{9}- \frac{108}{9}
=6769=(263)2\displaystyle = \frac{676}{9}= \left(\frac{26}{3}\right)^2

So b±b24ac2a=283±2632(1/3)\displaystyle \frac{-b\pm\sqrt{b^2- 4ac}}{2a}= \frac{-\frac{28}{3}\pm\frac{26}{3}}{2(1/3)}

Taking the "+", x=(283+263)(3/2)=(23)(32)=1\displaystyle x= (-\frac{28}{3}+ \frac{26}{3})(3/2)= \left(\frac{2}{3}\right)\left(\frac{3}{2}\right)= 1.

Taking the '-", x=(283263)(3/2)=(543)(32)=27\displaystyle x= (-\frac{28}{3}- \frac{26}{3})(3/2)= \left(\frac{54}{3}\right)\left(\frac{3}{2}\right)= 27.
 
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