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受欢迎的代数 >

solvefor r,(2-r)^2+(4-r)^2=(r+2)^2

解答

r, (2 - r)^{2} + (4 - r)^{2} = (r + 2)^{2}

解答

r = 4 (2 + 3), r = 4 (2 - 3)

+1

十进制

r = 14.92820 \dots, r = 1.07179 \dots

求解步骤

(2 - r)^{2} + (4 - r)^{2} = (r + 2)^{2}

展开

(2 - r)^{2} + (4 - r)^{2} : 2 r^{2} - 12 r + 20

展开

(r + 2)^{2} : r^{2} + 4 r + 4

2 r^{2} - 12 r + 20 = r^{2} + 4 r + 4

将

4

para o lado esquerdo

2 r^{2} - 12 r + 16 = r^{2} + 4 r

将

4 r

para o lado esquerdo

2 r^{2} - 16 r + 16 = r^{2}

将

r^{2}

para o lado esquerdo

r^{2} - 16 r + 16 = 0

使用求根公式求解

r_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 \cdot 1 \cdot 16}{2 \cdot 1}

(- 16)^{2} - 4 \cdot 1 \cdot 16 = 83

r_{1, 2} = \frac{- ( - 16 ) \pm 8 3}{2 \cdot 1}

将解分隔开

r_{1} = \frac{- ( - 16 ) + 8 3}{2 \cdot 1}, r_{2} = \frac{- ( - 16 ) - 8 3}{2 \cdot 1}

r = \frac{- ( - 16 ) + 8 3}{2 \cdot 1} : 4 (2 + 3)

r = \frac{- ( - 16 ) - 8 3}{2 \cdot 1} : 4 (2 - 3)

二次方程组的解是:

r = 4 (2 + 3), r = 4 (2 - 3)

作图

流行的例子

5.7614a^2+2593a-516461.55=0

5.7614 a^{2} + 2593 a - 516461.55 = 0

2 t^{2} + t - 3 = 0

- 12 x^{2} - 12 x = 0

r^{2} - 6 r + 14 = 0

49 n^{2} - 6 = 75