Final answer to the problem
$k=\frac{-1+\sqrt{33}}{2},\:k=\frac{-1-\sqrt{33}}{2}$
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Step-by-step Solution
Learn how to solve equations problems step by step online. Solve the quadratic equation 4+(2k^2-5k+1)^(1/2)=2+(k^2-2k+1)^(1/2). Group the terms of the equation by moving the terms that have the variable k to the left side, and those that do not have it to the right side. Subtract the values 2 and -4. The trinomial k^2-2k+1 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula.
Final answer to the problem
$k=\frac{-1+\sqrt{33}}{2},\:k=\frac{-1-\sqrt{33}}{2}$
