If x4 + 1/x4 = 194, (x > 0), then the value of (2x – 4)2 is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 12
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Concept |
Understanding |
Application |
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If a2 + 1/a2 = p then a + 1/a = √(p + 2) |
Given |
x4 + 1/x4 = 194 Then x2 + 1/x2 = √(194 + 2) x2 + 1/x2 = √196 = 14 Now, x + 1/x = √(14 + 2) x + 1/x = √16 x + 1/x = 4 Then x2 – 4x = -1 Now we need to find: (2x – 4)2 Which can be written as: 4(x – 2)2 = 4(x2 – 4x + 4) = 4(-1 + 4) = 12 |