Question
If x 8 Â + x -8 Â = 194, then find
the value of (2x 2  – 4) 2  – 1.Solution
Given, x 8 Â + x -8 Â = 194
Or, {x 4  + (1/x 4 )} 2  – 2 = 194 (Since, (a + b) 2  = a 2  + b 2  + 2ab)
Or, {x 4  + (1/x 4 )} = √(194 + 2)
Or, {x 4 Â + (1/x 4 )} = 14
Or, {x 2  + (1/x 2 )} 2  – 2 = 14 (Since, (a + b) 2  = a 2  + b 2  + 2ab)
Or, {x 2  + (1/x 2 )} = √(14 + 2)
Or, {x 2 Â + (1/x 2 )} = 4
Or, (x 4 Â + 1) = 4x 2
Or, x 4  – 4x 2  = -1
Also, (2x 2  – 4) 2  – 1
= 4x 4  – 16x 2  + 16 – 1
= 4(x 4  – 4x 2 ) + 15
= 4 × (-1) + 15 = 11
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