3. (a) Cardamo and Ferrari discovered that to depress a cubic, it is sufficient to let x = y − the equation ax³ + bx² + cx+d=0. * Depress the cubic 2x³ - 30x² + 162x − - 350 = 0. (b) To solve a depressed cubic of the form in x³ + Ax = B Scipione del Ferro noticed that it is sufficient to let 3st = A (& express s in terms of t) and s³t³ = B. A solution will be given by x = s-t. * Consider the depressed cubic x³ - 2x = 4. Write the s,t equations and solve for s and t. Find the associated solution.
3. (a) Cardamo and Ferrari discovered that to depress a cubic, it is sufficient to let x = y − the equation ax³ + bx² + cx+d=0. * Depress the cubic 2x³ - 30x² + 162x − - 350 = 0. (b) To solve a depressed cubic of the form in x³ + Ax = B Scipione del Ferro noticed that it is sufficient to let 3st = A (& express s in terms of t) and s³t³ = B. A solution will be given by x = s-t. * Consider the depressed cubic x³ - 2x = 4. Write the s,t equations and solve for s and t. Find the associated solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
(a) Cardamo and Ferrari discovered that to depress a cubic, it is sufficient to let x = y
the equation
ax³ + bx² + cx + d = 0.
* Depress the cubic 2x³ - 30x² + 162x - 350 = 0.
(b) To solve a depressed cubic of the form
T
x³ - 2x = 4.
Write the s,t equations and solve for s and t. Find the associated solution.
3a
.5
x³ + Ax = B
Scipione del Ferro noticed that it is sufficient to let 3st = A (& express s in terms of t) and
S³-t³ = B. A solution will be given by x = s — t.
* Consider the depressed cubic
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