Question

(2t-1)в крадрате -4t=13

Answer 1

(2t-1)²-4t=13
4t²-4t+1-4t=13
4t²-8t-12=0
t²-2t-3=0
D=2²+4*3=16=4²
t=(2-4)/2= -1 или t=(2+4)/2=3
ответ: -1 или 3

Answer 2

To solve the quadratic equation (2t-1)^2 - 4t = 13, we can follow these steps:

Step 1: Expand the squared term (2t-1)^2 using the formula (a-b)^2 = a^2 - 2ab + b^2. Step 2: Simplify the equation by combining like terms. Step 3: Move all terms to one side of the equation to set it equal to zero. Step 4: Factor the quadratic expression. Step 5: Use the zero-product property to solve for 't'.

Let's go through the steps:

Step 1: Expand the squared term: (2t - 1)^2 = (2t)^2 - 2 * 2t * 1 + 1 = 4t^2 - 4t + 1

Step 2: Simplify the equation: 4t^2 - 4t + 1 - 4t = 13

Step 3: Move all terms to one side of the equation: 4t^2 - 8t - 12 = 0

Step 4: Factor the quadratic expression: To factor this quadratic equation, we need to find two numbers whose product is (4 * -12) = -48 and whose sum is -8.

The numbers are -12 and +4 because (-12) * (+4) = -48 and (-12) + (+4) = -8.

So, we can rewrite the equation as: 4t^2 - 12t + 4t - 12 = 0

Step 5: Use the zero-product property to solve for 't': Now, factor the expression by grouping: (4t^2 - 12t) + (4t - 12) = 0 4t(t - 3) + 4(t - 3) = 0 (4t + 4)(t - 3) = 0

Now set each factor equal to zero and solve for 't':

1. 4t + 4 = 0 4t = -4 t = -4/4 t = -1

2. t - 3 = 0 t = 3

So, the solutions to the quadratic equation are t = -1 and t = 3.