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受欢迎的代数 >

solvefor λ,λ^2-2αλ+λ^2-1=0

解答

求解

λ, λ^{2} - 2 α λ + λ^{2} - 1 = 0

解答

λ = \frac{α + α ^{2} + 2}{2}, λ = \frac{α - α ^{2} + 2}{2}

求解步骤

λ^{2} - 2 α λ + λ^{2} - 1 = 0

展开

λ^{2} - 2 α λ + λ^{2} - 1 : - 2 λ α + 2 λ^{2} - 1

- 2 λ α + 2 λ^{2} - 1 = 0

改写成标准形式

a x^{2} + b x + c = 0

2 λ^{2} - 2 α λ - 1 = 0

使用求根公式求解

λ_{1, 2} = \frac{- ( - 2 α ) \pm ( - 2 α ) ^{2} - 4 \cdot 2 ( - 1 )}{2 \cdot 2}

化简

(- 2 α)^{2} - 4 \cdot 2 (- 1) : 2 α^{2} + 2

λ_{1, 2} = \frac{- ( - 2 α ) \pm 2 α ^{2} + 2}{2 \cdot 2}

将解分隔开

λ_{1} = \frac{- ( - 2 α ) + 2 α ^{2} + 2}{2 \cdot 2}, λ_{2} = \frac{- ( - 2 α ) - 2 α ^{2} + 2}{2 \cdot 2}

λ = \frac{- ( - 2 α ) + 2 α ^{2} + 2}{2 \cdot 2} : \frac{α + α ^{2} + 2}{2}

λ = \frac{- ( - 2 α ) - 2 α ^{2} + 2}{2 \cdot 2} : \frac{α - α ^{2} + 2}{2}

二次方程组的解是:

λ = \frac{α + α ^{2} + 2}{2}, λ = \frac{α - α ^{2} + 2}{2}

作图

流行的例子

- 3 x^{2} - 4 x + 6 = 0

6 - x^{2} = 3 - 2 x

solvefor x,b^2x^2-a^2y^2=a^2b^2

so l v e f or x, b^{2} x^{2} - a^{2} y^{2} = a^{2} b^{2}

1 0^{2} + x^{2} = 6^{2}

solvefor x,2x^2y=0

so l v e f or x, 2 x^{2} y = 0