Asked by kelvin calin
Which are the solutions of x2 = 19x + 1?
StartFraction 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 19 EndRoot Over 2 EndFraction
StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction
StartFraction negative 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 19 EndRoot Over 2 EndFraction
StartFraction negative 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 365 EndRoot Over 2 EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Solve x^2 = 19x + 1 → x^2 − 19x − 1 = 0. By the quadratic formula:
x = [19 ± √(19^2 − 4·1·(−1))]/2 = [19 ± √(361 + 4)]/2 = [19 ± √365]/2.
So the correct choice is:
(19 − √365)/2 and (19 + √365)/2.
x = [19 ± √(19^2 − 4·1·(−1))]/2 = [19 ± √(361 + 4)]/2 = [19 ± √365]/2.
So the correct choice is:
(19 − √365)/2 and (19 + √365)/2.
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