Given : $x : (m^{2} - 2 n) = Y : (m^{2} + 2 n)$ . Make n the subject of formula.
If $3 m = 5 x = y = 15$ , find the value of n.

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Solution

Given, $\frac{x}{y} = \frac{m^{2} - 2 n}{m^{2} + 2 n}$
$=> m^{2} x + 2 n x = m^{2} y - 2 n y$
$=> 2 n x + 2 n y = m^{2} y - m^{2} x$
$=> 2 n (x + y) = m^{2} (y - x)$
$=> n = \frac{m^{2} (y - x)}{2 (x + y)}$
When, $y = 15;$ and $3 m = 15 => m = 5$ , and $5 x = 15 => x = 3$ we get
$n = \frac{5^{2} (15 - 3)}{2 (3 + 15)} = \frac{25 \times 12}{2 \times 18} = 8 \frac{1}{3}$

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Similar questions

x : (m^{2} - 2 n) = y : (m^{2} + 2 n)

3 m = 5 x = y = 15

n = 8 \frac{1}{x}

x

m = 2 n + \sqrt{n^{2} + x},

x

n^{2}

\frac{10 - 3 x}{5 + 2 x} = \frac{m}{n}

3 m - 411 = 2

n = 2.5

3 m + n = 15

m + 2 n = 10

If 3m - 5m = -1 and 2m = n-3, find the value of (3m+5n) and (m+2n).

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