The discussion centers on solving the quartic equation y^4 + 4y - 69 = 0. Participants confirmed that y = -3 and y = 2.76 are solutions found through manual substitution. They noted the absence of straightforward analytical methods for quartic equations without advanced tools. Instead, they suggested using numerical methods like Newton's method for approximating solutions efficiently.
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You can't "solve" an expression. You can, however, solve an equation or inequality. Is the equation y^4 + 4y - 69 = 0?phillyolly said:Homework Statement
Solving y^4+4y-69
I don't know of any ways to solve quartic (fourth-degree) equations analytically, but there might be some. There are ways to solve cubics (third-degree), but even they are fairly involved to solve.phillyolly said:, I got the following:
By manually plugging in, I found that y= -3 and y=2.76.
However, I would like to ask you if there are other good, efficient ways to find solutions?
(Without using sophisticated math tools. Imagine, I have this prob on the exam)
Thank you!