solvefor x,z=x(x^2+y^2)^{1/2}

解答

求解

x, z = x (x^{2} + y^{2})^{\frac{1}{2}}

x = \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}

求解步骤

z = x (x^{2} + y^{2})^{\frac{1}{2}}

两边进行平方:

z^{2} = x^{4} + x^{2} y^{2}

z^{2} = x^{4} + x^{2} y^{2}

解

z^{2} = x^{4} + x^{2} y^{2} : x = \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}

x = \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} + ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}, x = - \frac{- y ^{2} - ( y ^{4} + 4 z ^{2} ) ^{\frac{1}{2}}}{2}

5 x - 6 = - 1

(x - 4)^{2} + (1 - x)^{2} = 7

10 x + x - 2 = 0

- x^{2} + 25 + x = 1

x = 5