Question:
If x2 - 12x + 1 = 0, then find the value of {x6 + x + x5 + 1}/x3
If x2 - 12x + 1 = 0, then find the value of {x6 + x + x5 + 1}/x3
Updated On: Sep 10, 2024
- 1870
- 1834
- 1830
- 1840
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The Correct Option is B
Solution and Explanation
Since, x2 - 12x + 1 = 0
Dividing each term by ‘x’, we get
x – 12 + 1/x = 0
Or, x + 1/x = 12 ................. (1)
Squaring both sides of equation (1), we get
x2 + 1/x2 + 2 × x × 1/x = 12 × 12
Or, x2 + 1/x2 = 144 - 2 = 142 ……………. (2)
Cubing both sides of equation (1), we get
x3 + 1/x3 + 3 × x × (1/x) × (x + 1/x) = 12 × 12 × 12 = 1728
Or, x3 + 1/x3 = 1728 - 3 × 12 = 1692
{x6 + x + x5 + 1}/x3 = (x3 + 1/x3) + (x2 + 1/x2) = 1692 + 142 = 1834
So, the correct option is (B) : 1834.
Dividing each term by ‘x’, we get
x – 12 + 1/x = 0
Or, x + 1/x = 12 ................. (1)
Squaring both sides of equation (1), we get
x2 + 1/x2 + 2 × x × 1/x = 12 × 12
Or, x2 + 1/x2 = 144 - 2 = 142 ……………. (2)
Cubing both sides of equation (1), we get
x3 + 1/x3 + 3 × x × (1/x) × (x + 1/x) = 12 × 12 × 12 = 1728
Or, x3 + 1/x3 = 1728 - 3 × 12 = 1692
{x6 + x + x5 + 1}/x3 = (x3 + 1/x3) + (x2 + 1/x2) = 1692 + 142 = 1834
So, the correct option is (B) : 1834.
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