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4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
The solution set of the equation ${x^{{{\log }_x}{{(1 - x)}^2}}} = 9$ is
  • ✓
    $\{-2, 4\}$
  • B
    $\{4\}$
  • C
    $\{0, -2, 4\}$
  • D
    None of these
✓

Answer

Correct option: A.
$\{-2, 4\}$
a
(a) ${x^{{{\log }_x}(1 - x)}}^2 = 9$

==>${\log _x}(9) = {\log _x}{(1 - x)^2}({a^x} = N\,\,\, $

$\Rightarrow {\log _a}N = x)$

==> $9 = {(1 - x)^2}\,\,\,$

$ \Rightarrow 1 + {x^2} - 2x - 9 = 0$

==> ${x^2} - 2x - 8 = 0$

==> $(x + 2)(x - 4) = 0$ ==> $x = - 2\,,4$.

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