1) what are the x-intercepts of the graph of y=12x^2 - 5x - 2?
2) What are the solutions to the equation 1+ 1/x^2 = 3/x?
2) What are the solutions to the equation 1+ 1/x^2 = 3/x?
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y = 12x² - 5x - 2 = 12x² - 8x + 3x - 2 = (4x + 1)(3x - 2)
so x intercepts are -1/4 and 2/3
1 + 1/x² = 3/x ∙ ∙ ∙ ∙ ∙ multiply by x² (assuming x <> 0)
x² + 1 = 3x
x² - 3x + 1 = 0 ∙ ∙ ∙ ∙ ∙quadratic formula
x = [3 ± √(9 - 4)] / 2
x = (3 ± √5) / 2
so x intercepts are -1/4 and 2/3
1 + 1/x² = 3/x ∙ ∙ ∙ ∙ ∙ multiply by x² (assuming x <> 0)
x² + 1 = 3x
x² - 3x + 1 = 0 ∙ ∙ ∙ ∙ ∙quadratic formula
x = [3 ± √(9 - 4)] / 2
x = (3 ± √5) / 2