If x4 + x-4 = 194, x > 0 then the value of (x – 2)2 is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3
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Concept |
Understanding |
Application |
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(x + x-1)2 = x2 + x-2 +2 |
Given: x4 + x-4 = 194, x > 0
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x4 + x-4 = 194 ⇒ x4 + x-4 + 2 = 194 + 2 ⇒ (x2 + x-2)2 = 196 ⇒ x2 + x-2 = 14 ⇒ x2 + x-2 + 2 = 14 + 2 ⇒ (x + x-1)2 = 16 ⇒ x + x-1 = 4 ⇒ x2 + 1 = 4x ⇒ x2 – 4x + 1 = 0 ⇒ x2 – 4x + 4 = 3 ⇒ (x – 2)2 = 3 |