Question

please solve it fast ​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ permissible \: values \: of \: x \\ \\ given \: that \\ x∈[ - 2\pi,3\pi] = [4\pi,3\pi] \\ \\ 3 \sqrt{3} ,2 \sqrt{2} .sin {}^{2} x,sin \: x \: are \: i n\: GP \\ \\ (2 \sqrt{2} .sin {}^{2} x) {}^{2} = 3 \sqrt{3} .sin \: x \\ 8.sin {}^{4} x = 3 \sqrt{ 3} .sin \: x \\ 8sin {}^{4} x - 3 \sqrt{3} .sin \: x = 0 \\ \\ sin \: x(8sin {}^{3} x - 3 \sqrt{3} ) = 0 \\ \\ sin \: x = 0 \: \: or \: \: sin {}^{3} x = \frac{3 \sqrt{3} }{8} \\ \\ sin \: x = 0 \: \: or \: \: sin \: x = \frac{2}{ \sqrt[3]{3 \sqrt{3} } } \\ \\ but \: as \: x \: lies \: between \: \\ quadrant \: 3\: and \: 4 \\ its \: range \: should \: not \: include \\ \: positive \: ratios \: \\ \\ hence \: then \\ sin \: x = \frac{2}{ \sqrt[3]{3 \sqrt{3} } } \: is \: rejected \\ \\ sin \: x = 0 \\ \\ x = 4\pi \: or \: x = 3\pi \\ ie \: would \: lie \: on \: x - axis \\ \\ no \: of \: solutions = 2$