Question

A) x^2+4>4(4x-15) б) (4x+3)(3x-2)>(12x-11)(x+1)

Answer 1

А) x^2+4>16x-60
x^2+4-16x+60>0
f(x)=0
f(x)=x^2-16x+64
x^2-16x+64=0
D=256-256=0 => 1 корень
x=-b\2a
x=16\2*1
x=8

Answer 2

Let's solve the inequalities one by one:

A) x^2 + 4 > 4(4x - 15)

Step 1: Expand and simplify the inequality: x^2 + 4 > 16x - 60

Step 2: Move all terms to one side of the inequality: x^2 - 16x + 64 > 0

Step 3: Factorize the quadratic equation: (x - 8)^2 > 0

Step 4: Analyze the inequality: Since (x - 8)^2 is always greater than or equal to zero for any value of x, except when x = 8, the solution to the inequality is: x ≠ 8

B) (4x + 3)(3x - 2) > (12x - 11)(x + 1)

Step 1: Expand and simplify the inequality: 12x^2 - 5x - 6 > 12x^2 + x - 11

Step 2: Move all terms to one side of the inequality: 12x^2 - 5x - 6 - 12x^2 - x + 11 > 0

Step 3: Combine like terms: -6x + 5 > 0

Step 4: Move constant to the other side of the inequality: -6x > -5

Step 5: Divide by a negative number (which reverses the inequality sign): x < 5/6

So, the solution to the inequality is: x < 5/6

Please note that for both inequalities, we have strict inequalities (i.e., > and not ≥), which means we don't include the boundary points in the solutions.