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

Assessment: WAEC SSCE - Further Mathematics - 2022 (Objective) Subject: Further Mathematics

Question 1 Report

x = -2 or x = 1

x = 0 or x = -3

x = 2 or x = 1

x = 0 or x = 3

Answer Details

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

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

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

let p = 3 $^{x}$

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

multiply through by 9
p $^{2}$ - 28p + 27 = 0
p $^{2}$ - 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 $^{x}$
3 $^{x}$ = 1
3 $^{x}$ = 3 $^{0}$
x = 0
when p = 27
3x = 27
3x = 33
x = 3

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Differentiation

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

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