Solve for x: 2^x+2^-x=2

### 2 Answers | Add Yours

The equation 2^x + 2^-x = 2 has to be solved.

2^x + 2^-x = 2

let y = 2^x

=> y + 1/y = 2

=> y^2 - 2y + 1 = 0

=> (y - 1)^2 = 0

=> y = 1

2^x = 1

=> x = 0

**The solution of the equation 2^x + 2^-x = 2 is x = 0**

2ˣ + 2⁻ˣ = 2

if, 2ˣ = ß

ß + 1/ß = 2

ß² + 1 = 2ß

ß² - 2ß + 1 = 0

(ß - 1)² = 0

ß - 1 = √0

ß - 1 = 0

ß = 1

Therefore 2ˣ = 1

**x = 0**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes