The equation \( x^{\frac{3}{4}\left(\log _{2} x\right)^{2}+\log _{2} x-\frac{5}{4}}=\sqrt{2} \) ...

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The equation \( x^{\frac{3}{4}\left(\log _{2} x\right)^{2}+\log _{2} x-\frac{5}{4}}=\sqrt{2} \) has
(a) atleast one real solution
(b) exactly three real solutions
(c) exactly one irrational solution
(d) complex roots
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