Total number of solutions for the equation $$x2$$−$$3sin$$⁡x−π$$6=3$$ is (where$$ [.] denotes the greatest integer $$function)

Question

Total number of solutions for the equation $$x2$$−$$3sin$$⁡x−π$$6=3$$ is   (where$$ [.] denotes  the greatest integer $$function)

Infinity Learn · Accepted Answer

Given that $$x2$$−$$3sinx$$−π$$6=3Given$$ equation can be written as $$x2$$−$$3=3sinx$$−π$$6Hence$$,  $$x2$$−$$3=$$−$$3$$,$$0$$,$$3$$⇒$$x=0$$,$$x=3$$ is only solution       if x $$=-3$$   then $$0=$$ $$sin$$ $$x-$$π$$6$$ ⇒ $$0$$≤$$sinx-$$π$$6$$<$$1$$ , which is not posible for $$x=-3$$                                                                similarly $$x=$$±$$6$$  does not satisfy the equation

$Total number of solutions for the equation x^{2} - 3 [\sin (x - \frac{π}{6})] = 3 is (where [.] denotes$ $the greatest integer function)$

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Total number of solutions for the equation x2−3sin⁡x−π6=3 is (where [.] denotes the greatest integer function)

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$Total number of solutions for the equation x^{2} - 3 [\sin (x - \frac{π}{6})] = 3 is (where [.] denotes$ $the greatest integer function)$