Question

X²-2x-1=0

The equation above has solutions x=n+√k and x=n-√k , where n and k are positive integers. What is the value of n+k ?

Answer 1

The solutions for x in the equation x²-2x-1=0 are x=1+√(2) and x=1-√(2). The value of n+k is 3.

Step-by-step explanation:

To find the value of n+k in the equation x²-2x-1=0, we need to solve for x. We can solve this quadratic equation by using the quadratic formula: x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a=1, b=-2, and c=-1. Let's plug these values into the formula:

x = (-(-2) ± √((-2)²-4(1)(-1)))/(2(1))

x = (2 ± √(4+4))/(2)

x = (2 ± √(8))/(2)

x = (2 ± 2√(2))/(2)

x = 1 ± √(2)

So the two solutions for x are x=1+√(2) and x=1-√(2). Now we can find the value of n+k. Since n and k are positive integers, n=1 and k=2. Therefore, n+k=1+2=3.