Solve: 3²x-2} - 28(3^{x-2}) + 3 = 0

Correct Answer is : x = 0 or x = 3

Correct Answer is : x = 0 or x = 3

Test Index

WAEC Further Mathematics 2022 Paper

Question : 24

Total: 45

Solve:

3^{2x-2} - 28(3^{x-2}) + 3 = 0

Solution:

$3^{2x-2} - 28(3^{x-2}) + 3 = 0$

$\frac{3^{2x}}{3^2} - \frac{28.3^x}{3^2} + 3 = 0$

$\frac{3^{2x}}{9} - \frac{28.3^x}{9} + 3 = 0$

let p = 3 $^{x}$

$\frac{p^{2}}{9} - \frac{28p}{9} + 3 = 0$

multiply through by 9

^{2}

- 28p + 27 = 0

^{2}

- p - 27p + 27 = 0

p (p - 1) - 27(p - 1) = 0

(p-1)(p-27) = 0

p = 1 or 27

when p = 1

p = 3

^{x}

^{x}

= 1

^{x}

= 3

^{0}

x = 0

when p = 27

3x = 27

3x = 33

x = 3

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