Question
x2 - 2x – 1 = 0
The equation above has solutions and where n and k are positive integers. What is the value of n + k ?
The correct answer is: 3
HINT: Solve the quadratic equation using quadratic formula.
Complete step by step solution:
Given quadratic equation is
We know that the Quadratic formula is
Here, b = - 2, a = 1, c = - 1
By substituting these values in the Quadratic formula,
We get
After simplification, we get .
The roots are, and which is of the form and respectively.
We get, n = 1 and k = 2.
So, n + k = 1 + 2 = 3
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