Question

1) 4(x1-1)^2-16x=0 2)4x^2-11x-7=0

Answer 1

1.  4(x1-1)^2-16x=0
4(x-1)^2 - 16x = 0
4(x^2 -2x+1)-16x=0
4x^2+24x+4=0
4(x^2-6x+1)=0
x^2-6x+1=0
D= 36 - 4 * 1 *1 = 36-4=32 
x = 6+- 4 √2/2  (4 корня из 2)
x1= 6+4√2/2=3+2√2 
x2= 6-4√2/2= 3-2√2 

2. 4x^2-11x-7=0
D= 121 - 4*4*(-7)= 121+112=233 
x= 11 +-√233/8
x1=11+√233/8
x2= 11-√233/8 

Answer 2

Это правильное решение!

Answer 3

To solve 4(x1-1)^2-16x=0, we can start by simplifying the expression:

4(x1-1)^2-16x = 0 4(x1^2-2x1+1) - 16x = 0 4x1^2 - 8x1 + 4 - 16x = 0 4x1^2 - 8x1 - 16x + 4 = 0 4x1^2 - 8x1 - 16x + 4 = 0

Next, we can combine like terms and move all terms to one side of the equation:

4x1^2 - 24x1 + 4 = 0

Now we can use the quadratic formula to solve for x1:

x1 = (-(-24) ± sqrt((-24)^2 - 4(4)(4))) / (2(4)) x1 = (24 ± sqrt(512)) / 8 x1 = (24 ± 16sqrt(2)) / 8 x1 = 3 ± 2sqrt(2)

Therefore, the solutions to the equation 4(x1-1)^2-16x=0 are x1 = 3 + 2sqrt(2) and x1 = 3 - 2sqrt(2).

To solve 4x^2-11x-7=0, we can again use the quadratic formula:

x = (-(-11) ± sqrt((-11)^2 - 4(4)(-7))) / (2(4)) x = (11 ± sqrt(169)) / 8 x = (11 ± 13) / 8

So the solutions to the equation 4x^2-11x-7=0 are x = 3/4 and x = -7/4.