Question

If (7m + 2n) / (7m - 2n) = 5/3, use properties of proportion to find
(i)- m:n
(ii)- (m²+n²) / (m²-n²)


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Answer 1

$\large\bf{\underline\orange{Answer \:↝}}$

Given

$\frac{7m + 2n}{7m - 2n} = \frac{5}{3}$

To Find :-

i) m : n

$\frac{7m + 2n}{7m - 2n} = \frac{5}{3}$

3(7m+2n) = 5(7m-2n)

21m + 6n = 35m - 10n

14m = 16n

$\frac{m}{n} = \frac{16}{14} = \frac{8}{7}$

m : n = 8 : 7

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

$\frac{ {8}^{2} + {7}^{2} }{{8}^{2} - {7}^{2}}$

$\frac{64 + 49}{64 - 49}$

$\frac{113}{15}$

Answer 2

Answer:

$\huge \red {answer}$

Given

\frac{7m + 2n}{7m - 2n} = \frac{5}{3}

7m−2n

7m+2n

=

3

5

To Find :-

i) m : n

\frac{7m + 2n}{7m - 2n} = \frac{5}{3}

7m−2n

7m+2n

=

3

5

3(7m+2n) = 5(7m-2n)

21m + 6n = 35m - 10n

14m = 16n

\frac{m}{n} = \frac{16}{14} = \frac{8}{7}

n

m

=

14

16

=

7

8

m : n = 8 : 7

ii) \frac{ ({m}^{2} + {n}^{2}) }{ ({m}^{2} - {n}^{2}) }

(m

2

−n

2

)

(m

2

+n

2

)

\frac{ {8}^{2} + {7}^{2} }{{8}^{2} - {7}^{2}}

8

2

−7

2

8

2

+7

2

\frac{64 + 49}{64 - 49}

64−49

64+49

\frac{113}{15}

15

113