Question

1) 9/х = х4) 4х⁴-5х²+1=06) (х²+х-3)-12(х²+х-3)+27=0​

Answer 1

Ответ :

На картинке ...

Answer 2

Let's solve each of the equations step by step:

1. 9/х = х To solve this equation, we'll isolate the variable 'x' on one side of the equation: 9/x = x

To do that, we'll first multiply both sides by 'x': 9 = x^2

Now, to find the value of 'x,' take the square root of both sides: x = ±√9

The solutions are: x = 3 and x = -3

2. 4x⁴ - 5x² + 1 = 0 This is a quadratic equation in terms of x^2. Let's make a substitution to simplify it: Let y = x², then the equation becomes: 4y² - 5y + 1 = 0

Now, we can factor this quadratic equation: (4y - 1)(y - 1) = 0

Set each factor to zero and solve for y:

1. 4y - 1 = 0 4y = 1 y = 1/4

2. y - 1 = 0 y = 1

Now, substitute back y = x² into each solution:

1. x² = 1/4 x = ±√(1/4) x = ±1/2

2. x² = 1 x = ±√1 x = ±1

The solutions to the original equation are: x = 1/2, x = -1/2, x = 1, and x = -1

3. (х² + х - 3) - 12(х² + х - 3) + 27 = 0 Let's make a substitution to simplify it: Let y = (x² + x - 3), then the equation becomes: y - 12y + 27 = 0

Combine like terms: -11y + 27 = 0

Now, solve for y: -11y = -27 y = 27/11

Substitute back y = (x² + x - 3) into the solution: x² + x - 3 = 27/11

To solve for 'x,' we need to bring everything to one side and make it a quadratic equation: x² + x - 3 - 27/11 = 0 x² + x - 3 - 3*11/11 = 0 x² + x - 36/11 = 0

Now, we can use the quadratic formula to find the solutions for 'x': x = [-b ± √(b² - 4ac)] / 2a

where a = 1, b = 1, and c = -36/11.

x = [-1 ± √(1 - 4*(1)(-36/11))] / 21 x = [-1 ± √(1 + 144/11)] / 2 x = [-1 ± √(11/11 + 144/11)] / 2 x = [-1 ± √(155/11)] / 2

The solutions to the equation are: x = [-1 + √(155/11)] / 2 and x = [-1 - √(155/11)] / 2

Note: You can simplify the solutions further by rationalizing the denominators if needed.