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(sqrt3 + sqrt2)^t + (sqrt3 - sqrt2)^t = 10: number of real solutions

The same question, asked 2 times: 1 Feb 2023*, 1 Feb 2024. Every wording below, oldest first.

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  1. Question 1

    1 Feb 2023

    77
    Let S={x:x∈RS =\left\{ x:x\in R \right. and  (3+2)x2−4+(3−2)x2−4=10}\left. \ (\sqrt{3}+\sqrt{2})^{x^{2}- 4}+ (\sqrt{3}-\sqrt{2})^{x^{2}- 4}= 10 \right\} Then n(S)n(S) is equal to

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  2. Question 2

    1 Feb 2024

    69
    Let S={x∈R:(3+2)x+(3−2)x=10}S =\left\{ x\in R:(\sqrt{3}+\sqrt{2})^{x}+ (\sqrt{3}-\sqrt{2})^{x}= 10 \right\}. Then the number of elements in SS is :

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