SOLUTION: find the ratio of a and b from the equation 12a^2 + 36b^2 -43ab=0

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Question 257458: find the ratio of a and b from the equation 12a^2 + 36b^2 -43ab=0
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the ratio of a and b from the equation
12a^2 + 36b^2 -43ab=0
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Rearrange
12a^2 - 43ab + 36b^2 = 0
Factor:
(4a-9b)(3a-4b) = 0
4a = 9b or 3a = 4b
a/b = 9/4 or a/b = 4/3
a:b = 9:4 or a:b = 4:3
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Cheers,
Stan H.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

12a%5E2+%2B+36b%5E2+-43ab=0

%284a-9b%29%283a-4b%29=0

Using the zero-factor principle:

4a-9b=0

4a=9b

Divide both sides ny 4b

%284a%29%2F%284b%29=%289b%29%2F%284b%29

%28cross%284%29a%29%2F%28cross%284%29b%29=%289cross%28b%29%29%2F%284cross%28b%29%29

a%2Fb=9%2F4

-------------------

3a-4b=0

3a=4b

Divide both sides ny 3b

%283a%29%2F%283b%29=%284b%29%2F%283b%29

%28cross%283%29a%29%2F%28cross%283%29b%29=%284cross%28b%29%29%2F%283cross%28b%29%29

a%2Fb=4%2F3

Edwin