Question

7a²+7b²÷7a²_7b²=113÷13value of a÷b?

Answer 1

GIVEN :–

$\\ \implies\bf \dfrac{7 {a}^{2} + 7 {b}^{2} }{7 {a}^{2} - 7 {b}^{2}} = \dfrac{113}{13}$

TO FIND :–

• Value of a/b = ?

SOLUTION :–

$\\ \implies\bf \dfrac{7 {a}^{2} + 7 {b}^{2} }{7 {a}^{2} - 7 {b}^{2}} = \dfrac{113}{13}$

$\\ \implies\bf \dfrac{7( {a}^{2} + {b}^{2} )}{7 ({a}^{2} - {b}^{2})} = \dfrac{113}{13}$

$\\ \implies\bf \dfrac{{a}^{2} + {b}^{2}}{{a}^{2} - {b}^{2}} = \dfrac{113}{13}$

• Use C & D rule –

$\\ \implies\bf \dfrac{({a}^{2} + {b}^{2}) + ({a}^{2} - {b}^{2})}{({a}^{2} + {b}^{2}) - ({a}^{2} - {b}^{2})} = \dfrac{113 + 13}{113 - 13}$

$\\ \implies\bf \dfrac{{a}^{2} + {b}^{2} + {a}^{2} - {b}^{2}}{{a}^{2} + {b}^{2} - {a}^{2} + {b}^{2}} = \dfrac{113 + 13}{113 - 13}$

$\\ \implies\bf \dfrac{{a}^{2} + {b}^{2} + {a}^{2} - {b}^{2}}{{a}^{2} + {b}^{2} - {a}^{2} + {b}^{2}} = \dfrac{126}{100}$

$\\ \implies\bf \dfrac{{a}^{2} + {a}^{2}}{{b}^{2}+ {b}^{2}} = \dfrac{126}{100}$

$\\ \implies\bf \dfrac{2{a}^{2}}{2{b}^{2}} = \dfrac{126}{100}$

$\\ \implies\bf \dfrac{{a}^{2}}{{b}^{2}} = \dfrac{126}{100}$

$\\ \implies\bf \bigg(\dfrac{a}{b} \bigg)^{2} = \dfrac{126}{100}$

$\\ \implies\bf \dfrac{a}{b}= \sqrt{\dfrac{126}{100}}$

$\\ \large\implies{ \boxed{\bf \dfrac{a}{b}= \dfrac{ \sqrt{126}}{10}}}$