Question 257458
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{{{12a^2 + 36b^2 -43ab=0}}}

{{{(4a-9b)(3a-4b)=0}}}

Using the zero-factor principle:

{{{4a-9b=0}}}

{{{4a=9b}}}

Divide both sides ny {{{4b}}}

{{{(4a)/(4b)=(9b)/(4b)}}}

{{{(cross(4)a)/(cross(4)b)=(9cross(b))/(4cross(b))}}}

{{{a/b=9/4}}}

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{{{3a-4b=0}}}

{{{3a=4b}}}

Divide both sides ny {{{3b}}}

{{{(3a)/(3b)=(4b)/(3b)}}}

{{{(cross(3)a)/(cross(3)b)=(4cross(b))/(3cross(b))}}}

{{{a/b=4/3}}}

Edwin</pre>