Question

Can anyone solve this

Answer 1

Answer:

From the given conditions we find that x is  $\frac{3}{2}$   and y is 0.

Step-by-step explanation:

In the question given the base is equal which is 2, so we can equate the powers to find the solution to the question.

We can write $\sqrt{8}$ as $2^{\frac{3}{2} }$.

We need to use this expression to solve the question, we will get two equations from the given conditions,solving them simultaneously we will get the final answer.

$2^{(x+y)} =\sqrt{8} \\2^{(x+y)} =2^{\frac{3}{2} } \\x+y=\frac{3}{2}$(i)

$2^{(x-y)} =2^{\frac{3}{2} }\\x-y=\frac{3}{2}$(ii)

Solving equations (i) and (ii) simultaneously, we have

$2x=\frac{3}{2} +\frac{3}{2} \\2x=3\\x=\frac{3}{2}$

Substituting value of x in equation (i)

$x+y=\frac{3}{2}\\\frac{3}{2}+y=\frac{3}{2}\\y=0$

Therefore the solution is, x=3/2 and y=0.