First slide

Theory of equations

Question

$Number of real solution(s) of the equation | x - 3 |^{3 x^{2} - 10 x + 3} = 1 is$

Moderate

A

Exactly four
B

exactly three
C

exactly two
D

exactly one

Solution

Given that
${|x - 3|}^{3 x^{2} - 10 x + 3} = 1$
Taking log on both sides
$(3 x^{2} - 10 x + 3) \log (|x - 3|) = 0$
$\Rightarrow \log (| x - 3 |) = 0 or 3 x^{2} - 10 x + 3 = 0$
$\Rightarrow x = 4, 2 or x = 3 (rejected) or \frac{1}{3}$
$∴ x = 2, 3, 4 are solutions$

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