Question

1.,,,,,,(4х+3)(5-х)-х^2 =8х+19 2.,,,,9х^2-(7х-2)(х+3)=-12х+1

Answer 1

20х-4хквадрат+15-3х-хквадрат=8х+19

20х-4хквадрат+15-3Х-Хквадрат-8Х-19=0

-5хквадрат+9х-4=0

Д=9 в квадрате-4*-5*-4=81-80=1

х1,2=-9+-1/2*-5=первый корень 0.8, а второй 1

Answer 2

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

1. (4x + 3)(5 - x) - x^2 = 8x + 19

Expanding the equation: (4x + 3)(5 - x) - x^2 = 8x + 19 (4x + 3)(5) + (4x + 3)(-x) - x^2 = 8x + 19 20x + 15 - 4x^2 - 3x - x^2 = 8x + 19

Rearranging the equation: -4x^2 - x^2 + 20x - 3x - 8x - 8x + 15 - 19 = 0 -5x^2 + x - 4 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring:

-5x^2 + x - 4 = 0 (-5x + 4)(x + 1) = 0

Setting each factor equal to zero: -5x + 4 = 0 or x + 1 = 0

Solving for x: -5x = -4 or x = -1

Dividing both sides by -5: x = 4/5

Therefore, the solutions to the equation are x = -1 and x = 4/5.

2. 9x^2 - (7x - 2)(x + 3) = -12x + 1

Expanding the equation: 9x^2 - (7x - 2)(x + 3) = -12x + 1 9x^2 - (7x^2 + 19x - 6) = -12x + 1 9x^2 - 7x^2 - 19x + 6 + 12x - 1 = 0 2x^2 - 7x + 5 = 0

This is another quadratic equation. Let's solve it by factoring:

2x^2 - 7x + 5 = 0 (2x - 1)(x - 5) = 0

Setting each factor equal to zero: 2x - 1 = 0 or x - 5 = 0

Solving for x: 2x = 1 or x = 5

Dividing both sides by 2: x = 1/2

Therefore, the solutions to the equation are x = 1/2 and x = 5.