Question

(3+х)^2+(3-2х)(5+2х)-3 (5-х)^2=1

Answer 1

9 + 6x + x^2  + 15 + 6x - 10x - 4x^2 - 3(25 - 10x + x^2) =  1
9 + 6x + x^2 + 15 + 6x - 10x - 4x^2 - 75 + 30x - 3x^2 - 1 = 0 
- 6x^2 + 32x - 52 = 0  // :  ( - 2)
3x^2 - 16x + 26 = 0 
D = - 56 
нет реш

Answer 2

Let's solve the equation step by step:

(3 + x)^2 + (3 - 2x)(5 + 2x) - 3(5 - x)^2 = 1

Expanding the squares: (9 + 6x + x^2) + (15 - 6x + 6x^2 + 10x - 4x^2) - (75 - 30x + 3x^2) = 1

Simplifying: 9 + 6x + x^2 + 15 - 6x + 6x^2 + 10x - 4x^2 - 75 + 30x - 3x^2 = 1

Combining like terms: (-3x^2 + 6x^2 - 4x^2) + (6x - 6x + 30x) + (9 + 15 - 75) = 1

Simplifying further: -1x^2 + 30x - 51 = 1

Rearranging the equation: x^2 - 30x + 52 = 0

Now, we have a quadratic equation. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -30, and c = 52. Substituting these values into the quadratic formula:

x = (-(-30) ± √((-30)^2 - 4(1)(52))) / (2(1))

Simplifying: x = (30 ± √(900 - 208)) / 2 x = (30 ± √692) / 2 x = (30 ± 2√173) / 2

Simplifying further: x = 15 ± √173

Therefore, the solutions to the equation are x = 15 + √173 and x = 15 - √173.