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

解

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

x = \frac{- a - b + ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}, x = \frac{- a - b - ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}; a \neq = 0

解答ステップ

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

解くとthe二次式

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

簡素化

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

x_{1, 2} = \frac{- ( a + b ) \pm ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}; a \neq = 0

解を分離する

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

x = \frac{- ( a + b ) + ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}} : \frac{- a - b + ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}

x = \frac{- ( a + b ) - ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}} : \frac{- a - b - ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}

二次equationの解:

x = \frac{- a - b + ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}, x = \frac{- a - b - ( a + b ) ^{2} + 4 a ^{2} b ^{2}}{2 a ^{2}}; a \neq = 0