Problem: If 4 x + 2 x = 1 4 x + 2 x ​ = 1 x x
Answer Choices:
A. is an integer
B. is fractional
C. is irrational
D. is imaginary
E. may have two different valuesSolution:
4 x + 2 x = 1 ∴ 4 x − 1 = − 2 x 4 x + 2 x ​ = 1 ∴ 4 x − 1 = − 2 x ​ 16 x 2 − 10 x + 1 = 0 ∴ x = 1 8 1 6 x 2 − 1 0 x + 1 = 0 ∴ x = 8 1 ​ x = 1 2 x = 2 1 ​ y = x ∴ 4 y 2 + 2 y − 1 = 0 y = x ​ ∴ 4 y 2 + 2 ​ y − 1 = 0 y = 2 2 8 , − 4 2 8 , x = y 2 = 1 8 , 1 2 y = 8 2 2 ​ ​ , 8 − 4 2 ​ ​ , x = y 2 = 8 1 ​ , 2 1 ​