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:

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

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

let p = 2 $^x$

p $^2$ - 5(p) + 4 = 0

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

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

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

p = 1 or 4

But p = 2 $^x$ = 1 or 4

2 $^x$ = 2 $^2$

x = 2

2 $^x$ = 2 $^0$ = 1

x = 0

Therefore, the values of x = 0 and 2

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