Question

if m/n- n/m =7/5 then solve m2/n2+n2/m2=?​

Answer 1

99/25

Step-by-step explanation:

Given:

$\dfrac{m}{n} - \dfrac{n}{m} = \dfrac{7}{5}$

To find:

$\dfrac{ {m}^{2} }{ {n}^{2} } + \dfrac{ {n}^{2}}{{m}^{2}}$

How to Solve ?

1) Square the given

2) Then use Formula [(a-b) ² = a²+b²- 2ab]

3) Just put the value, Simplify and get answer

Solution:

$\sf \frac{m}{n} - \frac{n}{m} = \frac{7}{5} \\ \\ \sf \: [Squaring \: both \: side] \\ \\ {( \frac{m}{n} - \frac{n}{m})}^{2} = { (\frac{7}{5}) }^{2} \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } - 2. \frac{m}{n}. \frac{n}{m} = \frac{49}{25} \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } - 2. \frac{ \cancel{m}}{ \cancel{n}}. \frac{ \cancel{n}} {\cancel{m}} = \frac{49}{25} \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } - 2 = \frac{49}{25} \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } = \frac{49}{25} + 2 \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } = \frac{49 + 50}{25} \\ \\ \sf \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } \: = \frac{99}{25} \\ \\ \sf \therefore \: Our \: required \: answer \: is \: \: \frac{ {m}^{2} }{ {n}^{2} } + \frac{ {n}^{2} }{ {m}^{2} } = \frac{99}{25}$