Question

Сегодня сдавала экзамен по математике в МГУ, и, думаю, испортила всё на первом же задании. Оно было таким: 9*x(в квадрате)+4х+9=(77 под корнем)*(1-х(в квадрате))

Answer 1

$9x^2+4x+9=\sqrt{77}(1-x^2)\\\\9x^2+4x+9-\sqrt{77}+\sqrt{77}x^2=0\\\\(9+\sqrt{77})x^2+4x+(9-\sqrt{77})=0\\\\D/4=(-2)^2-(9+\sqrt{77})(9-\sqrt{77})=4-(81-77)=4-4=0\\\\x_1=x_2=-\frac{2}{9+\sqrt{77}}=-\frac{9-\sqrt{77}}{2}$

Answer 2

$9 x^{2} +4x+9= \sqrt{77} (1- x^{2} ) \\ 9 x^{2} +4x+9= \sqrt{77}- \sqrt{77} x^{2} \\ 9 x^{2}+ \sqrt{77} x^{2} +4x+9- \sqrt{77}=0 \\ (9+ \sqrt{77} ) x^{2} +4x+9- \sqrt{77} =0 \\ D=16-4 (9+ \sqrt{77} ) (9- \sqrt{77} ) =16-4(81-77)=16-4*4=0 \\ \\ x= \frac{-4}{2*(9+ \sqrt{77} )} =- \frac{2}{(9+ \sqrt{77} )} =- \frac{2(9- \sqrt{77} )}{(9+ \sqrt{77} )(9- \sqrt{77} )} =- \frac{2(9- \sqrt{77} )}{81-77} = \\ \\ =- \frac{2(9- \sqrt{77} )}{4} =- \frac{9- \sqrt{77} }{2} = \frac{ \sqrt{77} -9}{2}$

$OTBET: \frac{ \sqrt{77} -9}{2}$

Answer 3

Solving the Equation

To solve the equation 9x^2 + 4x + 9 = (77 + sqrt(x)) * (1 - x^2), we can follow these steps:

1. Expand the right side of the equation: - (77 + sqrt(x)) * (1 - x^2) = 77 - 77x^2 + sqrt(x) - sqrt(x)x^2 2. Combine like terms: - 9x^2 + 4x + 9 = 77 - 77x^2 + sqrt(x) - sqrt(x)x^2

3. Rearrange the equation to bring all terms to one side: - 9x^2 + 4x + 9 - 77 + 77x^2 - sqrt(x) + sqrt(x)x^2 = 0 - Simplifying further, we get: - 86x^2 + 4x - 68 + sqrt(x)x^2 - sqrt(x) = 0

4. Solve the equation using numerical methods or algebraic techniques: - Unfortunately, the equation you provided is a complex equation involving both quadratic and square root terms. It does not have a simple algebraic solution. To find the solution, you can use numerical methods such as graphing, factoring, or using a calculator or computer program.

5. Use numerical methods to find the solution: - One way to find the solution is by using a graphing calculator or a computer program that can solve equations numerically. By graphing the equation or using numerical solvers, you can find the approximate values of x that satisfy the equation.

6. Seek assistance from a math tutor or professor: - If you are still having trouble solving the equation, it may be helpful to seek assistance from a math tutor or professor. They can guide you through the steps and provide additional explanations or techniques to solve the equation.

Remember, it's important to double-check your work and ensure that you have copied the equation correctly. Good luck with your exam results!