Question

If 2 power x+y = 2 power x-y = √8 then the value of y is?

Answer 1

Answer:It is 0.

Step-by-step explanation:=> 2power x+y= √8

=> 2power x+y=2power 3/2

=> x+y=3/2 [1]

=>2power x-y=2power 3/2

=>x-y=3/2 [2]

Add both eq.=

=>2x=6/2

=>x=3/2

In eq. 1=

=>3/2+y=3/2

=>y=0

Answer 2

Answer:

The value of 'y' is equal to zero.

Step-by-step explanation:

Given that $(2)^{x+y} =(2)^{x-y} =\sqrt{8}$

We have to find the value of 'y'

$(2)^{x+y}$ = (√8) = $(8)^{\frac{1}{2} } =(2^{3} )^{\frac{1}{2} } =(2)^{\frac{3}{2} }$

if (x)ᵃ = (x)ᵇ

⇒ a = b (∵ bases are same then powers are equal.)

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

⇒$x+y = \frac{3}{2}$ --------------(1)

$(2)^{x-y} = \sqrt{8\\} \\(2)^{x-y} =(8)^{\frac{1}{2} }$

$(2)^{x-y} =(2^{3} )^{\frac{1}{2} } =(2)^{\frac{3}{2} }$

⇒x - y = $\frac{3}{2}$ -----------(2)

Adding equation(1) and equation(2)

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

x + y + x - y = $\frac{6}{2}$

2x = 3

x =  $\frac{3}{2}$

Put x= $\frac{3}{2}$  in equation(1)

$\frac{3}{2}$ + y =  $\frac{3}{2}$

y =  $\frac{3}{2}$ -  $\frac{3}{2}$  = 0

Therefore, y = 0