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tamaranim1 [39]
3 years ago
8

Solve (2^2x+1)-9(2^x)+4=0​

Mathematics
1 answer:
BartSMP [9]3 years ago
8 0
  • Answer:

<em> x₁ = - 1</em>

<em> x₂ = 2</em>

  • Step-by-step explanation:

<em>2²ˣ⁺¹ - 9ₓ2ˣ + 4 = 0</em>

<em>2²ˣₓ2 - 9ₓ2ˣ + 4 = 0</em>

<em>2ˣ = n</em>

<em>2n² - 9n + 4 = 0</em>

<em>2n² - n - 8n + 4 = 0</em>

<em>n(2n - 1) - 4(2n - 1) = 0</em>

<em>(2n - 1)(n -4) = 0</em>

<em>2n - 1 = 0 => n₁ = 1/2</em>

<em>n - 4 = 0 => n₂ = 4</em>

<em />

<em>2ˣ = 1/2 => 2ˣ = 2⁻¹ => x₁ = - 1</em>

<em>2ˣ = 4 => 2ˣ = 2² => x₂ = 2</em>

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