Question

if 2^x+y=2^x-y=√8 find the value of y

Answer 1

-3/4 is the answer to the question

Answer 2

Value of y is zero.

Given:

• ${2}^{x + y} = {2}^{x - y} = \sqrt{8}$

To find:

• Find the value of y.

Solution:

Concept/formula to be used:

• If $\: {2}^{n} = {2}^{m}, \: then \: n = m$
• $\: ( {{2}^{n}})^m = {2}^{nm}$

Step 1:

Write equations.

${2}^{x + y} = \sqrt{8}$

or

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

or

$\bf x + y = \frac{3}{2} \: \: \: \: ...eq1$

and

${2}^{x - y} = \sqrt{8}$

or

$\bf x - y = \frac{3}{2} \: \: ...eq2$

Step 2:

Solve eq1 and eq2.

$x + y = \frac{3}{2} \\ x - y = \frac{3}{2} \\ ( - ) \: \: ( + ) \: \: ( - )\\ - - - - - - - \\ 2y = 0 \\ - - - - - - -$

or

$\bf y = 0$

Thus,

Value of y is zero.

Learn more:

1) On Simplifying 8^3×2^4, we get. (a) 16^7 (b) 2^10 (c) 2 ^13 (d) 8^4

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