2/T = cos cos--Cos 4. 16 12+2cos 7/2 /2+2 cos a /4 V2 +2 cos T /16 elido vZ VZ+ vZ V2+ V2+ v2 2+ V2 + v2 12. Vièta solved the quadratic equation x2 +ax = b by substituting x = y – a/2. This produces a quadratic in y in which the first-degree term is missing. Use Vièta's method to solve the quadratic equations: %3D %3D - x² + 8x = 9. x² + 10x = 144. (b) x² +12x = 64. (c) 3x² + 10x = 32. [Hint: Multiply both sides by 3 (d) and let z = 3.x.] barieh (a) %3D %3D %3D %3D 7). 13. To solve the equation x² + ax = b² geometrically, René Descartes would have used the method as Mndi described. Draw a line segment AB of length b and at A erect a perpendicular AC of length a/2. With C as center, construct a circle of radius a /2 and draw a line through B and C , intersecting the circle at points D and E. Prove that the length of the segment BE is the value of x that satisfies x² +ax = b². %D until

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Topic Video
Question

Number 12

2/T = cos cos--Cos
4.
16
12+2cos 7/2
/2+2 cos a /4
V2 +2 cos T /16
elido
vZ VZ+ vZ V2+ V2+ v2
2+ V2 + v2
12. Vièta solved the quadratic equation x2 +ax = b by
substituting x = y – a/2. This produces a quadratic in
y in which the first-degree term is missing. Use Vièta's
method to solve the quadratic equations:
%3D
%3D
-
x² + 8x = 9.
x² + 10x = 144.
(b)
x² +12x = 64.
(c)
3x² + 10x = 32. [Hint: Multiply both sides by 3
(d)
and let z = 3.x.]
barieh (a)
%3D
%3D
%3D
%3D
7).
13. To solve the equation x² + ax = b² geometrically,
René Descartes would have used the method as
Mndi
described. Draw a line segment AB of length b and at
A erect a perpendicular AC of length a/2. With C as
center, construct a circle of radius a /2 and draw a line
through B and C , intersecting the circle at points D
and E. Prove that the length of the segment BE is the
value of x that satisfies x² +ax = b².
%D
until
Transcribed Image Text:2/T = cos cos--Cos 4. 16 12+2cos 7/2 /2+2 cos a /4 V2 +2 cos T /16 elido vZ VZ+ vZ V2+ V2+ v2 2+ V2 + v2 12. Vièta solved the quadratic equation x2 +ax = b by substituting x = y – a/2. This produces a quadratic in y in which the first-degree term is missing. Use Vièta's method to solve the quadratic equations: %3D %3D - x² + 8x = 9. x² + 10x = 144. (b) x² +12x = 64. (c) 3x² + 10x = 32. [Hint: Multiply both sides by 3 (d) and let z = 3.x.] barieh (a) %3D %3D %3D %3D 7). 13. To solve the equation x² + ax = b² geometrically, René Descartes would have used the method as Mndi described. Draw a line segment AB of length b and at A erect a perpendicular AC of length a/2. With C as center, construct a circle of radius a /2 and draw a line through B and C , intersecting the circle at points D and E. Prove that the length of the segment BE is the value of x that satisfies x² +ax = b². %D until
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