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受欢迎的代数 >

solvefor t,g(t-1)=5-(t-1)^2

解答

求解

t, g (t - 1) = 5 - (t - 1)^{2}

解答

t = - \frac{- 2 + g + g ^{2} + 20}{2}, t = - \frac{- 2 + g - g ^{2} + 20}{2}

求解步骤

g (t - 1) = 5 - (t - 1)^{2}

展开

g (t - 1) : t g - g

展开

5 - (t - 1)^{2} : - t^{2} + 2 t + 4

t g - g = - t^{2} + 2 t + 4

交换两边

- t^{2} + 2 t + 4 = t g - g

将

g

para o lado esquerdo

- t^{2} + 2 t + 4 + g = t g

将

t g

para o lado esquerdo

- t^{2} + 2 t + 4 + g - t g = 0

改写成标准形式

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

- t^{2} + (2 - g) t + 4 + g = 0

使用求根公式求解

t_{1, 2} = \frac{- ( 2 - g ) \pm ( 2 - g ) ^{2} - 4 ( - 1 ) ( 4 + g )}{2 ( - 1 )}

化简

(2 - g)^{2} - 4 (- 1) (4 + g) : g^{2} + 20

t_{1, 2} = \frac{- ( 2 - g ) \pm g ^{2} + 20}{2 ( - 1 )}

将解分隔开

t_{1} = \frac{- ( 2 - g ) + g ^{2} + 20}{2 ( - 1 )}, t_{2} = \frac{- ( 2 - g ) - g ^{2} + 20}{2 ( - 1 )}

t = \frac{- ( 2 - g ) + g ^{2} + 20}{2 ( - 1 )} : - \frac{- 2 + g + g ^{2} + 20}{2}

t = \frac{- ( 2 - g ) - g ^{2} + 20}{2 ( - 1 )} : - \frac{- 2 + g - g ^{2} + 20}{2}

二次方程组的解是:

t = - \frac{- 2 + g + g ^{2} + 20}{2}, t = - \frac{- 2 + g - g ^{2} + 20}{2}

作图

流行的例子

solvefor x,f(x-2)=x^2+4x+7

so l v e f or x, f (x - 2) = x^{2} + 4 x + 7

2 x^{2} - 3 x + 1 = 38

solvefor y,x^2+y^2=Ce^{2x}

so l v e f or y, x^{2} + y^{2} = C e^{2 x}

t^{2} - 5 = 3

0.15 x^{2} = 0.6