Question

已知3减根号2是方程X平方加MX加7等于零的一个根,则M的等于?另一根等于?

Answer 1

x1 + x2 = -M ==> M = -(x1 +x2) = - [(3-√2) + (3+√2)] = -6 x1 * x2 = 7 ==> x2 = 7 / (3 - √2) = 3+√2 追问：x2 = 7 / (3 - √2) = 3+√2中,7 / (3 - √2)如何计算 ,回答：7 / (3 - √2) = [7 * (3 + √2)] / [ (3 - √2) * (3 + √2)] = [7 * (3 + √2)] / [3^2 - (√2)^2] = [7 * (3 + √2)] / [9 - 2] = [7 * (3 + √2)] / 7 = (3 + √2) 追问：为什么要在分子与分母同乘 (3 + √2),去分母不是只需同乘 (3 - √2)吗?回答：分子与分母同乘 (3 + √2),是为了将 分母有理化 .分子与分母同乘(3 - √2),分母还是 无理数 .