Question

pls answer to my question​

Answer 1

Answer:

Use the property of duplicate ratio and simplify. Please see the steps given below.

Step-by-step explanation:

Duplicate ratio means the ratio compounded to itself.

Given,

m:n = duplicate ratio of m + x : n + x

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

$\frac{m}{n} = \frac{ {m}^{2} + 2mx + {x}^{2} }{ {n}^{2} + 2nx + {x}^{2} }$

Cross multiplying,

$m {n}^{2} + 2mnx + m {x}^{2} = n {m}^{2} + 2nmx + n {x}^{2}$

$m {n}^{2} + m {x}^{2} =n {m}^{2} + n {x}^{2}$

$(m - n) {x}^{2} = n {m}^{2} - m {n}^{2}$

$(m - n) {x}^{2} = mn(m - n)$

${x}^{2} = mn$