Question

It's urgent.... can some one solve this ​

Answer 1

Answer:

5 is the correct answer

Answer 2

Step-by-step explanation:

Question:-

$\rm If\: \: \dfrac{3 {a}^{2} +2 {b}^{2} }{2 {b}^{2} - {a}^{2} } = \dfrac{15}{7} \: \: and \: \: {a}^{2} : {b}^{2} = m : n. \: Then \: m - n = ......$

To Find:-

• The value of m-n

Solution:-

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

By cross multiplication:-

$\dashrightarrow \rm 7(3 {a}^{2} +2 {b}^{2}) = 15(2 {b}^{2} - {a}^{2} )$

$\dashrightarrow \rm 21 {a}^{2} +14 {b}^{2} = 30 {b}^{2} - 15{a}^{2}$

$\dashrightarrow \rm 21 {a}^{2} +15{a}^{2} = 30 {b}^{2} - 14{b}^{2}$

$\dashrightarrow \rm36{a}^{2} = 16 {b}^{2}$

$\dashrightarrow \rm \dfrac{ {a}^{2} }{ {b}^{2} } = \dfrac{16}{36}$

$\dashrightarrow \rm \dfrac{ {a}^{2} }{ {b}^{2} } = \dfrac{4}{9}$

$\dashrightarrow \rm { {a}^{2} } : { {b}^{2} } = {4} : {9}$

$\rm Given , \: { {a}^{2} } : { {b}^{2} } = m :n$

$\rm Comparing, \: { {a}^{2} } : { {b}^{2} } = m :n \: (with) \: { {a}^{2} } : { {b}^{2} } = {4} : {9}$

$\rm \dashrightarrow m = 4 \: \: and \: \: n = 9$

Now, we have to find the Value of m - n

$\rm \dashrightarrow m - n \: = \: 4 - 9 \: = \: - 5$

$\underline{ \boxed{ \purple{\rm \therefore m - n \: = \: - 5}}}$