Math CentralQuandaries & Queries


Question from Sabbie, a student:

Hi, I need help solving this equation for my physics homework,so I can solve the quadratic equations for x and y.
I've derived the following equations from the information provided in the question.

2a+3b = 4 -- 1
2a^2 + 3b^2 = 62 -- 2

a=2-(3/2)b is substituted into equation 2.

so, i get
2 (2-(3/2)b)^2 + 3b^2 = 62

this is where the problem begins. i cannot work through this to get to the correct quadratic equation


I can't seem to be able to figure out where I keep going wrong. I would really appreciate it if you could give me a step-by-step breakdown of the workout.



Expanding (2-(3/2)b)^2 I get

equation 1

and thus the equation becomes

equation 2

I then multiplied both sides by 2 and collected terms to get

15b2 - 24b - 108.

Finally dividing both sides by 3 gives the desired equation.


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