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if x + 1/x = 2 , then what is the value of x⁹⁵ + 1/x⁹⁵.
Asked by ria102680 | 19 May, 2022, 07:41: AM
Expert Answer
x + 1/x = 2
x2 + 1/x2 + 2 = 4
Therefore, x2 + 1/x2 = 2
x4 + 1/x4 + 2 = 4
x4 + 1/x4 = 2
Similarly, x8 + 1/x8 = 2
So, x32 + 1/x32 = 2
Thus, x64 + 1/x64 = 2
Now, (x31 + 1/x31)(x64 + 1/x64)= x95 + 1/x33 + x33 + 1/x95
x95 + 1/x95 = (x31 + 1/x31)(x64 + 1/x64) - (1/x33 + x33)
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