fortheentries
New member
- Joined
- Jan 6, 2023
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Hi everyone. I'm just revising some quadratics in preparation for tutoring high school maths and came across something about fractions that has made me question whether I've been learning maths wrong my entire life. I was solving a quadratic by completing the square for this question:
[math]x^2-(3/2)x=0[/math]
Obviously to complete the square I would have to add:
[math](\frac{b}{2})^2[/math]
Subbing in b I got:
[math]x^2-(3/2)x+(\frac{\frac{3}{2}}{2})^2= (\frac{\frac{3}{2}}{2})^2[/math]
I've always thought for this type of issue where you have a fraction div by a fraction you multiply by the reciprocal so to evaluate the b/2 section:
[math](\frac{3}{2}*\frac{2}{1})^2 \\ (\frac{6}{2})^2\\ 3^2= 9[/math]However, the worked answers display the b/2 section working as
[math](\frac{3}{2*2})^2[/math]
Which is correct?
[math]x^2-(3/2)x=0[/math]
Obviously to complete the square I would have to add:
[math](\frac{b}{2})^2[/math]
Subbing in b I got:
[math]x^2-(3/2)x+(\frac{\frac{3}{2}}{2})^2= (\frac{\frac{3}{2}}{2})^2[/math]
I've always thought for this type of issue where you have a fraction div by a fraction you multiply by the reciprocal so to evaluate the b/2 section:
[math](\frac{3}{2}*\frac{2}{1})^2 \\ (\frac{6}{2})^2\\ 3^2= 9[/math]However, the worked answers display the b/2 section working as
[math](\frac{3}{2*2})^2[/math]
Which is correct?