Question

if 3asquare+2bsquare/2bsquare-asquare=15/7 and a square : b square =m:n , then m-n=

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{\dfrac{3\,a^{2}+2\,b^2 }{2\,b^2-a^2}=\dfrac{15}{7}}$

Applying componendo and dividendo,

$\sf{\dfrac{3\,a^{2}+2\,b^2+2\,b^2-a^2 }{3\,a^{2}+2\,b^2-2\,b^2+a^2}=\dfrac{15}{7}}$

$\sf{\implies\,\dfrac{2\,a^{2}+4\,b^2 }{4\,a^{2}}=\dfrac{15}{7}}$

$\sf{\implies\,\dfrac{a^{2}+2\,b^2 }{2\,a^{2}}=\dfrac{15}{7}}$

$\sf{\implies\,7\,a^{2}+14\,b^2= 30\,a^{2}}$

$\sf{\implies\,14\,b^2= 23\,a^{2}}$

$\sf{\implies\dfrac{a^{2}}{b^2}=\dfrac{14}{ 23}}$

But given that, $\sf{\dfrac{a^2}{b^2}=\dfrac{m}{n}}$

So,

$\sf{\implies\dfrac{m}{n}=\dfrac{14}{ 23}}$

$\sf{\implies\,m-n=14- 23=-9}$