If a/b = 7/3 then find the value of the following ratio 2a^2+3b^2 / 2a^2-3b^2
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If a/b = 7/3 then find the value of the following ratio 2a^2+3b^2 / 2a^2-3b^2
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Answer:
125 : 71
Step-by-step explanation:
given, [tex]\frac{a}{b}[/tex] = [tex]\frac{7}{3}[/tex]
on squaring both sides,
=> [tex]\frac{a^2}{b^2}[/tex] = [tex]\frac{7^2}{3^2}[/tex]
=> [tex]\frac{a^2}{b^2}[/tex] = [tex]\frac{49}{9}[/tex]
=> [tex]\frac{a^2}{b^2}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{49}{9}[/tex] * [tex]\frac{2}{3}[/tex]
=> [tex]\frac{2a^2}{3b^2}[/tex] = [tex]\frac{98}{27}[/tex]
=> [tex]\frac{2a^2}{3b^2}[/tex] = [tex]\frac{98}{27}[/tex]
then by compendo-dividendo rule,
=> [tex]\frac{2a^2+3b^2}{2a^2-3b^2}[/tex] = [tex]\frac{98+27}{98-27}[/tex]
=> [tex]\frac{2a^2+3b^2}{2a^2-3b^2}[/tex] = [tex]\frac{125}{71}[/tex]
=> in ratio form , [tex]\frac{2a^2+3b^2}{2a^2-3b^2}[/tex] = 125 : 71
Verified answer
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