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I understand the quadratic formula. I can derive the quadratic formula. I do not understand what to do when b= the sum of two square roots, as in the following problem:
Use the quadratic formula to solve:
r squared + [square root (3) - square root (2)]*r = square root (6)
r^2+(√(3)-√(2))r = √(6)
I know the answer is r = -(√(3)) or √(2). I don't know how to get to that answer. I have tried a number of ways. Plugging a, b, and c straight into the quadratic formula, I get:
r = 1/2[√(2)-√(3)+√(5+(2√(6)))] or 1/2[√(2)-√(3)-√(5+(2√(6)))]
This is right, but I don't understand the following steps:
1/2[√(2)-√(3)+√(5+(2√(6)))] --> √(2)
1/2[√(2)-√(3)-√(5+(2√(6)))] --> -(√(3))
Thanks for your help! (I've been working on this problem for WAY too long.)
This answer helped me solve the problem! Thank you. The question answered here is a little different from mine. This question answers r^2+(√(3)+√(2))r = √(6) instead of r^2+(√(3)-√(2))r = √(6), but it was really helpful as an example format to use to solve the latter question. The key that I was missing was factoring √((√3)^2 + 2√(3)√(2) + (√(2))^2) ---> √((√(3) + √(2))^2). Thank you again!