Question

Найти наибольший корень уравнения .

Answer 1

ОДЗ x≠-2
log(3)(3^9*|x+2|)=log(3)(x+2)^4
3^9*|x+2|=(x+2)^4
1)x<-2
-3^9*(x+2)=(x+2)^4
(x+2)³=-3^9
x+2=-27
x=-29
2)x>-2
3^9*(x+2)=(x+2)^4
(x+2)³=3^9
x+2=27
x=25
Ответ х=-29;х=25

Answer 2

Finding the Largest Root of an Equation

To find the largest root of the equation, we can use the quadratic formula and the discriminant to determine the nature of the roots and then find the largest root.

The given equation is in the form of \(ax^2 + bx + c = 0\), where: - \(a = 6\) - \(b = -15\) - \(c = 4\)

Using the Quadratic Formula and Discriminant

The quadratic formula is given by: \[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]

The discriminant (\(D\)) is given by: \[D = b^2 - 4ac\]

Calculating the Discriminant

Using the values of \(a\), \(b\), and \(c\), we can calculate the discriminant: \[D = (-15)^2 - 4*6*4\] \[D = 225 - 96\] \[D = 129\]

Nature of the Roots

The nature of the roots is determined by the discriminant: - If \(D > 0\), the equation has two distinct real roots. - If \(D = 0\), the equation has two equal real roots. - If \(D < 0\), the equation has two complex roots.

Calculating the Roots

Using the quadratic formula, we can calculate the roots: \[x = \frac{{-(-15) \pm \sqrt{{129}}}}{{2*6}}\] \[x = \frac{{15 \pm \sqrt{{129}}}}{{12}}\]

The roots are: \[x_1 = \frac{{15 + \sqrt{{129}}}}{{12}} \approx 1.416\] \[x_2 = \frac{{15 - \sqrt{{129}}}}{{12}} \approx -0.416\]

Conclusion

The largest root of the equation is approximately 1.416.