Question

If x=2^2m and y=2^2m+1 find the value of (x+y)/(x-y)

Answer 1

Answer:

- 3

Step-by-step explanation:

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

${a}^{m + n} = {a}^{m} \times {a}^{n}$

GIVEN

$x = {2}^{2m} \: \: and \: \: y = {2}^{2m + 1}$

TO DETERMINE

$\displaystyle \: \frac{x + y}{x - y}$

EVALUATION

$x = {2}^{2m} \:$

$\: y = {2}^{2m + 1} = 2 \times {2}^{2m }$

So

$x + y$

$= {2}^{2m} + {2}^{2m + 1}$

$= {2}^{2m} + 2 \times {2}^{2m}$

$= 3 \times {2}^{2m}$

Again

$x - y$

$= {2}^{2m} - {2}^{2m + 1}$

$= {2}^{2m} - 2 \times {2}^{2m}$

$= - {2}^{2m}$

Hence

$\displaystyle \: \frac{x + y}{x - y} = \frac{3 \times {2}^{2m}}{ - {2}^{2m}} = - 3$