Question

При каких значениях x верно равенство x2−7=4x?

Answer 1

x²-4x-7=0

D=16+28= 44

x1= (4+√44)/2= 2+√11

x2= (4-√44)/2= 2-√11

При x=2±√11

Answer 2

To find the values of x that satisfy the equation x^2 - 7 = 4x, we need to solve the quadratic equation for x. First, let's rewrite the equation in the standard quadratic form:

x^2 - 4x - 7 = 0

Now, to solve for x, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -4, and c = -7.

x = (4 ± √((-4)^2 - 4 * 1 * (-7))) / 2 * 1

x = (4 ± √(16 + 28)) / 2

x = (4 ± √44) / 2

Now, let's find the two possible values for x:

1. x = (4 + √44) / 2 x = (4 + √4 * √11) / 2 x = (4 + 2√11) / 2 x = 2 + √11

2. x = (4 - √44) / 2 x = (4 - √4 * √11) / 2 x = (4 - 2√11) / 2 x = 2 - √11

So, the two values of x that satisfy the equation x^2 - 7 = 4x are:

1. x = 2 + √11
2. x = 2 - √11