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受欢迎的代数 >

solvefor y,(x+y)^3=x^3+y^3

解答

求解

y, (x + y)^{3} = x^{3} + y^{3}

解答

y = 0, y = - x; x \neq = 0

求解步骤

(x + y)^{3} = x^{3} + y^{3}

展开

(x + y)^{3} : x^{3} + 3 y x^{2} + 3 y^{2} x + y^{3}

x^{3} + 3 y x^{2} + 3 y^{2} x + y^{3} = x^{3} + y^{3}

将

y^{3}

para o lado esquerdo

x^{3} + 3 y x^{2} + 3 y^{2} x = x^{3}

将

x^{3}

para o lado esquerdo

3 y x^{2} + 3 y^{2} x = 0

改写成标准形式

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

3 x y^{2} + 3 x^{2} y = 0

使用求根公式求解

y_{1, 2} = \frac{- 3 x ^{2} \pm ( 3 x ^{2} ) ^{2} - 4 \cdot 3 x \cdot 0}{2 \cdot 3 x}

化简

(3 x^{2})^{2} - 4 \cdot 3 x \cdot 0 : 3 x^{2}

y_{1, 2} = \frac{- 3 x ^{2} \pm 3 x ^{2}}{2 \cdot 3 x}; x \neq = 0

将解分隔开

y_{1} = \frac{- 3 x ^{2} + 3 x ^{2}}{2 \cdot 3 x}, y_{2} = \frac{- 3 x ^{2} - 3 x ^{2}}{2 \cdot 3 x}

y = \frac{- 3 x ^{2} + 3 x ^{2}}{2 \cdot 3 x} : 0

y = \frac{- 3 x ^{2} - 3 x ^{2}}{2 \cdot 3 x} : - x

二次方程组的解是:

y = 0, y = - x; x \neq = 0

作图

流行的例子

x^{2} + 8 x + 16 = - 81

2 x^{2} + 3 x = 3

x^{2} + 8 x + 16 = - 64

(x+3)^2+x^2=269

(x + 3)^{2} + x^{2} = 269

(x-2)^2=(2x-3)^2-1

(x - 2)^{2} = (2 x - 3)^{2} - 1