MCQ
સમીકરણ ${\log _4}\{ {\log _2}(\sqrt {x + 8} - \sqrt x )\} = 0$ નું વાસ્તવિક બીજ..........છે.
- ✓$1$
- B$2$
- C$3$
- D$4$
$ \Rightarrow {4^0} = {\log _2}\left( {\sqrt {x + 8} - \sqrt x } \right)$
$ \Rightarrow {2^1} = \sqrt {x + 8} - \sqrt x $
$ \Rightarrow 4 = x + 8 + x - 2\sqrt {{x^2} + 8x} $
$ \Rightarrow 2\sqrt {{x^2} + 8x} = 2x + 4$
$ \Rightarrow {x^2} + 8x = {x^2} + 4 + 4x$
$ \Rightarrow 4x = 4$ $ \Rightarrow x = 1$
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