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人気のある代数 >

u(2u-1)a+(u-1)(2u-1)b+4u(1-u)c=0

解

u (2 u - 1) a + (u - 1) (2 u - 1) b + 4 u (1 - u) c = 0

解

u = \frac{a + 3 b - 4 c + b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}, u = \frac{a + 3 b - 4 c - b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}; 2 a + 2 b - 4 c \neq = 0

解答ステップ

u (2 u - 1) a + (u - 1) (2 u - 1) b + 4 u (1 - u) c = 0

拡張

u (2 u - 1) a + (u - 1) (2 u - 1) b + 4 u (1 - u) c : 2 a u^{2} - a u + 2 b u^{2} - 3 b u + b + 4 c u - 4 c u^{2}

2 a u^{2} - a u + 2 b u^{2} - 3 b u + b + 4 c u - 4 c u^{2} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

(2 a + 2 b - 4 c) u^{2} + (- a - 3 b + 4 c) u + b = 0

解くとthe二次式

u_{1, 2} = \frac{- ( - a - 3 b + 4 c ) \pm ( - a - 3 b + 4 c ) ^{2} - 4 ( 2 a + 2 b - 4 c ) b}{2 ( 2 a + 2 b - 4 c )}

簡素化

(- a - 3 b + 4 c)^{2} - 4 (2 a + 2 b - 4 c) b : b^{2} - 2 ab - 8 b c + a^{2} + 16 c^{2} - 8 a c

u_{1, 2} = \frac{- ( - a - 3 b + 4 c ) \pm b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}; 2 a + 2 b - 4 c \neq = 0

解を分離する

u_{1} = \frac{- ( - a - 3 b + 4 c ) + b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}, u_{2} = \frac{- ( - a - 3 b + 4 c ) - b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}

u = \frac{- ( - a - 3 b + 4 c ) + b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )} : \frac{a + 3 b - 4 c + b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}

u = \frac{- ( - a - 3 b + 4 c ) - b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )} : \frac{a + 3 b - 4 c - b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}

二次equationの解:

u = \frac{a + 3 b - 4 c + b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}, u = \frac{a + 3 b - 4 c - b ^{2} - 2 ab - 8 b c + a ^{2} + 16 c ^{2} - 8 a c}{2 ( 2 a + 2 b - 4 c )}; 2 a + 2 b - 4 c \neq = 0

グラフ

人気の例

0 = x^{2} - 10 x + 16

0 = x^{2} - 10 x + 18

solvefor x,p(x^2+3x+9)=x-x^2

so l v e f or x, p (x^{2} + 3 x + 9) = x - x^{2}

- 5 x^{2} + 7 = 0

quadraticformula-10t^2-12t=-9982

q u a d r a t i c f or m u l a - 10 t^{2} - 12 t = - 9982