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受欢迎的代数 >

(2x+5)^6=(1-x)^6

解答

(2 x + 5)^{6} = (1 - x)^{6}

解答

x = - 6, x = - \frac{4}{3}

+1

十进制

x = - 6, x = - 1.33333 \dots

求解步骤

(2 x + 5)^{6} = (1 - x)^{6}

展开

(2 x + 5)^{6} : 64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625

展开

(1 - x)^{6} : 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625 = 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

两边减去

1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625 - (1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}) = 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6} - (1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6})

化简

63 x^{6} + 966 x^{5} + 5985 x^{4} + 20020 x^{3} + 37485 x^{2} + 37506 x + 15624 = 0

因式分解

63 x^{6} + 966 x^{5} + 5985 x^{4} + 20020 x^{3} + 37485 x^{2} + 37506 x + 15624 : 7 (x + 6) (3 x + 4) (3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93)

7 (x + 6) (3 x + 4) (3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 6 = 0 or 3 x + 4 = 0 or 3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93 = 0

解

x + 6 = 0 : x = - 6

解

3 x + 4 = 0 : x = - \frac{4}{3}

解

3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93 = 0 : x \in R

无解

解为

x = - 6, x = - \frac{4}{3}

作图

流行的例子

(3 x - 7)^{3} + 1 = 5

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