Solve 2²x} - 5(2^x) + 4 = 0

Correct Answer is : x = 0 and 2

Correct Answer is : x = 0 and 2

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WAEC Further Mathematics 2024 Paper

Question : 11

Total: 40

Solve 2

^{2x}

^x

) + 4 = 0

Solution:

Concept:

Treat

2^x

as a single variable to turn the exponential equation into a quadratic equation.

Explanation:

Given:

2^{2x} - 5(2^x) + 4 = 0

Rewrite

2^{2x}

(2^x)^2

(2^x)^2 - 5(2^x) + 4 = 0

Let

p = 2^x

. Then the equation becomes:

p^2 - 5p + 4 = 0

Factorise the quadratic:

p^2 - 4p - p + 4 = 0

p(p - 4) - 1(p - 4) = 0

(p - 1)(p - 4) = 0

So,

p = 1 \quad \text{or} \quad p = 4

Since

p = 2^x

2^x = 1 \quad \text{or} \quad 2^x = 4

Now,

2^x = 1 = 2^0 \Rightarrow x = 0

2^x = 4 = 2^2 \Rightarrow x = 2

Answer:

x = 0

and

x = 2

Option A.

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