Maths-
General
Easy

Question

x2 - 2x – 1 = 0
The equation above has solutions x equals n plus square root of k and x equals n minus square root of k 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 x squared minus 2 x minus 1 equals 0
    We know that the Quadratic formula is fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    Here, b = - 2, a = 1, c = - 1
    By substituting these values in the Quadratic formula,
    We get  x equals fraction numerator negative left parenthesis negative 2 right parenthesis plus-or-minus square root of left parenthesis negative 2 right parenthesis squared minus left parenthesis 4 cross times 1 cross times negative 1 right parenthesis end root over denominator 2 cross times 1 end fraction equals fraction numerator 2 plus-or-minus square root of 8 over denominator 2 end fraction equals fraction numerator 2 plus-or-minus 2 square root of 2 over denominator 2 end fraction
    After simplification, we get x equals 1 plus-or-minus square root of 2.
    The roots are, 1 plus square root of 2and 1 minus square root of 2 which is of the form n plus square root of k and n minus square root of k respectively.
    We get, n = 1 and k = 2.
    So, n + k = 1 + 2 = 3
     

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