Question

plz solve this question​

Answer 1

Answer:

given equation : 8×2²ˣ + 4 × 2ˣ⁺¹ = 1 + 2ˣ

=> 8 × 2²ˣ + 4 x 2ˣ x 2¹ = 1 + 2ˣ

=> 8 x 2²ˣ + 8 x 2ˣ = 1 + 2ˣ

let a = 2ˣ

the equation reduces to

8a² + 8a = 1 + a

=> 8a² + 8a - a - 1 = 0

=> 8a² + 7a - 1 = 0

=> 8a² + 8a - a - 1 = 0

=> 8a (a + 1) - 1 (a + 1) = 0

=> (8a - 1)(a + 1) = 0

=> 8a - 1 = 0 or a = 1/8

=> a + 1 = 0 or a = -1

when a = 1/8

1/8 = 2ˣ => 1/2³ = 2ˣ => 2⁻³ = 2ˣ

=> - 3 = x => x = - 3