Question

If x/y=2/3 then (x-y/y)^2 is equal to?

Answer 1

Answer:

Required numeric value of { ( x - y ) / y }^2 is 1 / 9.

Step-by-step explanation:

Given,

$\dfrac{x}{y}=\dfrac{2}{3}$

Method 1

$\implies \bigg(\dfrac{x-y}{y}\bigg)^2$

Multiply the denominator and numerator by 1 / y :

$\implies \bigg( \dfrac{\frac{x-y}{y}}{\frac{y}{y}}\bigg)^2\\\\\\\implies\bigg(\dfrac{\frac{x}{y}-\frac{y}{y}}{\frac{y}{y}}\bigg)^2\\\\\\\implies\bigg(\dfrac{\frac{x}{y}-1}{1}\bigg)^2$

Substituting the value of x / y :

$\implies \bigg(\dfrac{2}{3}-1\bigg)^2\\\\\\\implies\bigg(\dfrac{2-3}{3}\bigg)^2\\\\\\\implies \bigg(\dfrac{-1}{3}\bigg)^2\\\\\\\implies\dfrac{1}{9}$

Method 2

$\implies \bigg(\dfrac{x-y}{y}\bigg)^2\\\\\\ \implies \bigg( \dfrac{x}{y}-\dfrac{y}{y}\bigg)^2\\\\\\\implies\bigg(\dfrac{2}{3}-1\bigg)^2\\\\\\\implies\bigg(\dfrac{2-3}{3}\bigg)^2\\\\\\\implies\bigg(\dfrac{-1}{3}\bigg)^2\\\\\\\implies\dfrac{1}{9}$

Hence the required numeric value of { ( x - y ) / y }^2 is 1 / 9.

Answer 2

$\dfrac{x}{y}$ = $\dfrac{2}{3}$

___________ [GIVEN]

• We have to find the value of ${( \dfrac{x \: - \: y}{y} )}^{2}$

_____________________________

$\implies$ ${( \dfrac{x \: - \: y}{y} )}^{2}$

$\implies$ ${( \dfrac{x }{y} \: - \: \dfrac{y}{y} )}^{2}$

$\implies$ ${( \dfrac{x }{y} \: - \: 1)}^{2}$

$\implies$ ${( \dfrac{2 }{3} \: - \: 1)}^{2}$

$\implies$ ${( \dfrac{2 \: - \: 3}{3} )}^{2}$

$\implies$ ${( \dfrac{-1}{3} )}^{2}$

_____________________________

${( \dfrac{x \: - \: y}{y} )}^{2}$ = $\dfrac{1}{9}$

______________ $\bold{[ANSWER]}$