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受欢迎的代数 >

17^2=w^2+(3w+9)^2

解答

1 7^{2} = w^{2} + (3 w + 9)^{2}

解答

w = \frac{13}{5}, w = - 8

+1

十进制

w = 2.6, w = - 8

求解步骤

1 7^{2} = w^{2} + (3 w + 9)^{2}

展开

1 7^{2} : 289

展开

w^{2} + (3 w + 9)^{2} : 10 w^{2} + 54 w + 81

289 = 10 w^{2} + 54 w + 81

交换两边

10 w^{2} + 54 w + 81 = 289

将

289

para o lado esquerdo

10 w^{2} + 54 w - 208 = 0

使用求根公式求解

w_{1, 2} = \frac{- 54 \pm 5 4 ^{2} - 4 \cdot 10 ( - 208 )}{2 \cdot 10}

5 4^{2} - 4 \cdot 10 (- 208) = 106

w_{1, 2} = \frac{- 54 \pm 106}{2 \cdot 10}

将解分隔开

w_{1} = \frac{- 54 + 106}{2 \cdot 10}, w_{2} = \frac{- 54 - 106}{2 \cdot 10}

w = \frac{- 54 + 106}{2 \cdot 10} : \frac{13}{5}

w = \frac{- 54 - 106}{2 \cdot 10} : - 8

二次方程组的解是:

w = \frac{13}{5}, w = - 8

作图

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