We are given: 7m+2n7m 2n=53 Use Componendo Dividendo: (7m+2n)+(7m 2n)(7m+2n) (7m 2n)=5+35 3 7m2n=4 mn=87 m^2+n^2m^2 n^2=(mn)^2+1(mn)^2 1 ...

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Ratio and Proportion

m2+n2/m2-n2.

Question

$\frac{m^{2} + n^{2}}{m^{2} - n^{2}}$ .

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Solution

We are given:
$\frac{7 m + 2 n}{7 m - 2 n} = \frac{5}{3}$
Use Componendo-Dividendo:
$\frac{(7 m + 2 n) + (7 m - 2 n)}{(7 m + 2 n) - (7 m - 2 n)} = \frac{5 + 3}{5 - 3}$

$⟹ \frac{7 m}{2 n} = 4$
$⟹ \frac{m}{n} = \frac{8}{7}$

$\frac{m^{2} + n^{2}}{m^{2} - n^{2}} = \frac{(\frac{m}{n})^{2} + 1}{(\frac{m}{n})^{2} - 1}$

$= \frac{64 + 49}{64 - 49} = \frac{113}{15}$

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s i n α - s i n β = m

c o s α c o s β = n

c o s (α - β) =

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