Question

Решите уравнения:a) (x-2)^2-x^2=12b)(2x+3)^2-4(x-1) (x+1) =49Срочно ​

Answer 1

Ответ:

Объяснение:

1)(x-2)²-x²=12

x²-4x+4-x²=12

-4x=12-4

-4x=8

x=-2

2) (2x+3)²-4(x-1)(x+1)=49

4x²+12x+9-4(x²-1)=49

4x²+12x+9-4x²+4=49

12x=49-9-4

12x=36

x=3

Answer 2

Solving the Equations:

a) (x-2)^2 - x^2 = 12

To solve this equation, let's expand and simplify the left-hand side:

(x-2)^2 - x^2 = 12 x^2 - 4x + 4 - x^2 = 12 -4x + 4 = 12 -4x = 12 - 4 -4x = 8 x = -2

b) (2x+3)^2 - 4(x-1) + (x+1) = 49

Similarly, let's expand and simplify the left-hand side of the equation:

(2x+3)^2 - 4(x-1) + (x+1) = 49 4x^2 + 12x + 9 - 4x + 4 + x + 1 = 49 4x^2 + 12x + 9 - 4x + 4 + x + 1 - 49 = 0 4x^2 + 9x - 35 = 0

Now, we can solve the quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4, b = 9, and c = -35.

Using the quadratic formula, we get:

x = (-9 ± √(9^2 - 4*4*(-35))) / (2*4) x = (-9 ± √(81 + 560)) / 8 x = (-9 ± √641) / 8

So, the solutions for the equation are:

x = (-9 + √641) / 8 and x = (-9 - √641) / 8

These are the solutions for the given equations.