Question : If $4x^{2}=15^{2}–9^{2}$, then the value of $x$ is:
Option 1: 9
Option 2: 6
Option 3: 3
Option 4: 12
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Correct Answer: 6
Solution : Given: $4x^{2}=15^{2}–9^{2}$ According to the formula of $a^{2}–b^{2}=(a–b)(a+b)$, ⇒ $4x^{2}=(15–9)(15+9)$ ⇒ $4x^{2}=6×24$ ⇒ $x^{2}=6×6$ ⇒ $x=\sqrt{36}$ ⇒ $x=6$ Hence, the correct answer is 6.
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Question : If $x+\frac{1}{x}=1$, then the value of $x^{12}+x^9+x^6+x^3+1$ is:
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