Maths · Arithmetic and Geometric progressions
If then
If \( x+\frac{1}{x}=3, \) then \( x^{4}+\frac{1}{x^{4}}= \)
- A. 81
- B. 23
- C. 25
- D. 47
Step-by-step solution
Given x + 1/x = 3. Square both sides: (x + 1/x)^2 = 9 ⇒ x^2 + 2 + 1/x^2 = 9 ⇒ x^2 + 1/x^2 = 7. Square again: (x^2 + 1/x^2)^2 = 49 ⇒ x^4 + 2 + 1/x^4 = 49 ⇒ x^4 + 1/x^4 = 47.
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