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標題:

A. maths(F.4)

發問:

Let r = (x+1)/(x^2+x+1). Find the range of values of r for all real values of x. Why the answer is -1/3 smaller or equal than r greater than or equal 1

最佳解答:

r = (x + 1) / (x^2 + x + 1) r(x^2 + x + 1) = x + 1 rx^2 + rx + r - x - 1 = 0 rx^2 + (r - 1)x + (r - 1) = 0.................(*) As x is a real number, for suitable values of r, (*) must have real roots. Thus discriminant ≥ 0 (r - 1)^2 - 4r(r - 1) ≥0 (r - 1)[(r - 1 - 4r)] ≥ 0 (r - 1)(-3r - 1) ≥ 0 (r - 1)(3r + 1) ≤ 0 -1 / 3 ≤ r ≤ 1

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其他解答:

r = (x + 1) / (x^2 + x + 1) r(x^2 + x + 1) = x + 1 rx^2 + rx + r - x - 1 = 0 rx^2 + (r - 1)x + (r - 1) = 0.................(*) As x is a real number, for suitable values of r, (*) must have real roots. Thus discriminant ≥ 0 (r - 1)^2 - 4r(r - 1) ≥0 (r - 1)[(r - 1 - 4r)] ≥ 0 (r - 1)(-3r - 1) ≥ 0 (r - 1)(3r + 1) ≤ 0 -1 / 3 ≤ r ≤ 1 希望幫到你 求你選我最佳答案 求下你 唔該!!!!!! 唔該!!!!!!