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If x2 + 1 = 6x, then what will be the value of (x6 + 1) / (x4 – 4x3 + x2)?

If x2 + 1 = 6x, then what will be the value of (x6 + 1) / (x4 – 4x3 + x2)? Correct Answer 99

Given: x2 + 1 = 6x

Calculation: x2 + 1 = 4x + 2x

x2 – 4x + 1 = 2x      ----(1)

Now,

(x6 + 1) / (x4 – 4x3 + x2)

(x6 + 1) /

(x4 + 1/x2) / (x2 – 4x + 1)

From equation (1)∶

(x4 + 1/x2) / (2x)

x(x3 + 1/x3) / (2x)

(1/2)      ----(2)

Now, again from x2 + 1 = 6x

(x2 + 1)/x = 6

x + 1/x = 6

From equation (2)∶

(1/2) × (216 – 18) = 99

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