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受欢迎的代数 >

3(t^2-9)^2+16(t^2-9)=-5

解答

3 (t^{2} - 9)^{2} + 16 (t^{2} - 9) = - 5

解答

t = \frac{26}{3}, t = - \frac{26}{3}, t = 2, t = - 2

+1

十进制

t = 2.94392 \dots, t = - 2.94392 \dots, t = 2, t = - 2

求解步骤

3 (t^{2} - 9)^{2} + 16 (t^{2} - 9) = - 5

展开

3 (t^{2} - 9)^{2} + 16 (t^{2} - 9) : 3 t^{4} - 38 t^{2} + 99

3 t^{4} - 38 t^{2} + 99 = - 5

将

5

para o lado esquerdo

3 t^{4} - 38 t^{2} + 104 = 0

用

u = t^{2}

和

u^{2} = t^{4}

改写方程式

3 u^{2} - 38 u + 104 = 0

解

3 u^{2} - 38 u + 104 = 0 : u = \frac{26}{3}, u = 4

u = \frac{26}{3}, u = 4

代回

u = t^{2}

，求解

t

解

t^{2} = \frac{26}{3} : t = \frac{26}{3}, t = - \frac{26}{3}

解

t^{2} = 4 : t = 2, t = - 2

解为

t = \frac{26}{3}, t = - \frac{26}{3}, t = 2, t = - 2

作图

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