a^2b^2x^2-(a^2+b^2)x+1=0

解

a^{2} b^{2} x^{2} - (a^{2} + b^{2}) x + 1 = 0

x = \frac{1}{b ^{2}}, x = \frac{1}{a ^{2}}; a^{2} b^{2} \neq = 0

解答ステップ

a^{2} b^{2} x^{2} - (a^{2} + b^{2}) x + 1 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - a ^{2} - b ^{2} ) \pm ( - a ^{2} - b ^{2} ) ^{2} - 4 a ^{2} b ^{2} \cdot 1}{2 a ^{2} b ^{2}}

簡素化

(- a^{2} - b^{2})^{2} - 4 a^{2} b^{2} \cdot 1 : (a + b) (a - b)

x_{1, 2} = \frac{- ( - a ^{2} - b ^{2} ) \pm ( a + b ) ( a - b )}{2 a ^{2} b ^{2}}; a^{2} b^{2} \neq = 0

解を分離する

x_{1} = \frac{- ( - a ^{2} - b ^{2} ) + ( a + b ) ( a - b )}{2 a ^{2} b ^{2}}, x_{2} = \frac{- ( - a ^{2} - b ^{2} ) - ( a + b ) ( a - b )}{2 a ^{2} b ^{2}}

x = \frac{- ( - a ^{2} - b ^{2} ) + ( a + b ) ( a - b )}{2 a ^{2} b ^{2}} : \frac{1}{b ^{2}}

x = \frac{- ( - a ^{2} - b ^{2} ) - ( a + b ) ( a - b )}{2 a ^{2} b ^{2}} : \frac{1}{a ^{2}}

二次equationの解:

x = \frac{1}{b ^{2}}, x = \frac{1}{a ^{2}}; a^{2} b^{2} \neq = 0