If x² - 5x + 1 = 0, then the value of x³ + 1/x³ is:

March 23, 2026Mathematics

ScanSolve AI Answer

March 23, 2026

Answer

Given: $x^{2} - 5x + 1 = 0$

Step 1: Divide both sides by $x$ (note $x \neq 0$ since the constant term is $1 \neq 0$ ).

$\frac{x^{2}}{x} - \frac{5x}{x} + \frac{1}{x} = \frac{0}{x}$

$x - 5 + \frac{1}{x} = 0$

Step 2: Isolate the target expression.

$x + \frac{1}{x} - 5 = 0$

$x + \frac{1}{x} = 5$

Answer: 3) 5

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Given: x^2 - 5x + 1 = 0 Step 1: Divide both sides by x (note x ≠ 0 since the constant term is 1 ≠ 0).

Asked on March 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 23, 2026

Given: x^2 - 5x + 1 = 0 Step 1: Divide both sides by x (note x ≠ 0 since the constant term is 1 ≠ 0). x^2x - (5x)/(x) + (1)/(x) = (0)/(x) x - 5 + (1)/(x) = 0 Step 2: Isolate the target expression. x + (1)/(x) - 5 = 0 x + (1)/(x) = 5 Answer: 3) 5 5