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人気のある代数 >

a(x-5)^2+b(x-2)(x-5)+(x-2)^2=0

解

a (x - 5)^{2} + b (x - 2) (x - 5) + (x - 2)^{2} = 0

解

x = \frac{10 a + 7 b + 4 + 3 b ^{2} - 4 a}{2 ( a + b + 1 )}, x = \frac{10 a + 7 b + 4 - 3 b ^{2} - 4 a}{2 ( a + b + 1 )}; a + b + 1 \neq = 0

解答ステップ

a (x - 5)^{2} + b (x - 2) (x - 5) + (x - 2)^{2} = 0

拡張

a (x - 5)^{2} + b (x - 2) (x - 5) + (x - 2)^{2} : a x^{2} - 10 a x + 25 a + b x^{2} - 7 b x + 10 b + x^{2} - 4 x + 4

a x^{2} - 10 a x + 25 a + b x^{2} - 7 b x + 10 b + x^{2} - 4 x + 4 = 0

標準的な形式で書く

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

(a + b + 1) x^{2} - (10 a + 7 b + 4) x + 25 a + 10 b + 4 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 10 a - 7 b - 4 ) \pm ( - 10 a - 7 b - 4 ) ^{2} - 4 ( a + b + 1 ) ( 25 a + 10 b + 4 )}{2 ( a + b + 1 )}

簡素化

(- 10 a - 7 b - 4)^{2} - 4 (a + b + 1) (25 a + 10 b + 4) : 3 b^{2} - 4 a

x_{1, 2} = \frac{- ( - 10 a - 7 b - 4 ) \pm 3 b ^{2} - 4 a}{2 ( a + b + 1 )}; a + b + 1 \neq = 0

解を分離する

x_{1} = \frac{- ( - 10 a - 7 b - 4 ) + 3 b ^{2} - 4 a}{2 ( a + b + 1 )}, x_{2} = \frac{- ( - 10 a - 7 b - 4 ) - 3 b ^{2} - 4 a}{2 ( a + b + 1 )}

x = \frac{- ( - 10 a - 7 b - 4 ) + 3 b ^{2} - 4 a}{2 ( a + b + 1 )} : \frac{10 a + 7 b + 4 + 3 b ^{2} - 4 a}{2 ( a + b + 1 )}

x = \frac{- ( - 10 a - 7 b - 4 ) - 3 b ^{2} - 4 a}{2 ( a + b + 1 )} : \frac{10 a + 7 b + 4 - 3 b ^{2} - 4 a}{2 ( a + b + 1 )}

二次equationの解:

x = \frac{10 a + 7 b + 4 + 3 b ^{2} - 4 a}{2 ( a + b + 1 )}, x = \frac{10 a + 7 b + 4 - 3 b ^{2} - 4 a}{2 ( a + b + 1 )}; a + b + 1 \neq = 0

グラフ

人気の例

log_{10}(9)(x-1)^2=1

lo g_{10} (9) (x - 1)^{2} = 1

4[4(x+1)(x+2)+2(x-1)^2]=11(2-x)-x(5+8x)

4 [4 (x + 1) (x + 2) + 2 (x - 1)^{2}] = 11 (2 - x) - x (5 + 8 x)

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

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

9 x^{2} + a = a^{2} x + a

2(x-3x^2)+5x(x-2)+9=-8x

2 (x - 3 x^{2}) + 5 x (x - 2) + 9 = - 8 x