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JEE Advance - Mathematics (1985 - No. 10)

Solve for $$x$$ ; $${\left( {5 + 2\sqrt 6 } \right)^{{x^2} - 3}} + {\left( {5 - 2\sqrt 6 } \right)^{{x^2} - 3}} = 10$$
$$x = \pm 2$$
$$x = \pm \sqrt{2}$$
$$x = 0$$
$$x = 1$$
No real solutions

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