Question

1) х^2-6х^2=6-х 2) у^3+3у^2-4y-12=0 Решите уравнение!!!

Answer 1

Ответ:

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Answer 2

1. To solve the equation х^2 - 6х^2 = 6 - х, first combine like terms on the left side of the equation:

-x^2 = 6 - х

Next, move all terms to one side to get the equation in standard form:

x^2 - х - 6 = 0

Now, we have a quadratic equation of the form ax^2 + bx + c = 0, where a = 1, b = -1, and c = -6.

To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values into the formula:

x = (1 ± √((-1)^2 - 4 * 1 * (-6))) / 2 * 1 x = (1 ± √(1 + 24)) / 2 x = (1 ± √25) / 2 x = (1 ± 5) / 2

Now, consider both cases:

1. x = (1 + 5) / 2 x = 6 / 2 x = 3

2. x = (1 - 5) / 2 x = -4 / 2 x = -2

The solutions to the equation are x = 3 and x = -2.

2. To solve the equation у^3 + 3у^2 - 4y - 12 = 0, we can try to factor it or use numerical methods to find the roots.

By inspection, we can see that y = 2 is one of the roots. We can then use polynomial long division or synthetic division to factor out the quadratic equation and find the other roots.

Using synthetic division:

2 | 1 3 -4 -12 | 2 10 12

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1 5 6 0

The result is the quadratic equation y^2 + 5y + 6 = 0.

Now, we have a quadratic equation of the form ay^2 + by + c = 0, where a = 1, b = 5, and c = 6.

To solve the quadratic equation, we can use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values into the formula:

y = (-5 ± √(5^2 - 4 * 1 * 6)) / 2 * 1 y = (-5 ± √(25 - 24)) / 2 y = (-5 ± √1) / 2

Now, consider both cases:

1. y = (-5 + 1) / 2 y = -4 / 2 y = -2

2. y = (-5 - 1) / 2 y = -6 / 2 y = -3

The solutions to the equation are y = 2, y = -2, and y = -3.