Question

find the ab ratio 18a2 + 20b2 -39ab =0

Answer 1

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Answer 2

Answer: The answer is 5 : 6 or 4 : 3.

Step-by-step explanation:  We are to find the ratio of 'a' and 'b' from the following equation:

$18a^2-39ab+20b^2=0.$

For that, first we should try to factorise the left hand side of the above equation.

We have

$18a^2-39ab+20b^2=0\\\\\Rightarrow 18a^2-24ab-15ab+20b^2=0\\\\\Rightarrow 6a(3a-4b)-5b(3a-4b)=0\\\\\Rightarrow (6a-5b)(3a-4b)=0.$

Therefore,

$6a-5b=0\\\\\Rightarrow 6a=5b\\\\\Rightarrow \dfrac{a}{b}=\dfrac{5}{6}\\\\\Rightarrow a:b=5:6,$

or

$3a-4b=0\\\\\Rightarrow 3a=4b\\\\\Rightarrow \dfrac{a}{b}=\dfrac{4}{3}\\\\\Rightarrow a:b=4:3.$

So, the ratio of a and b is 5 : 6 or 4 : 3.