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Deduce that if (b) Let a 2 cos 2 and ß = 2 cos 4. Show that a = @ +w4 and B=w² +0³. Find a quadratic equation with roots a,ß. Hence show that 27=(√5-1). 7. (a) Show that x-1=(x-1)(x²+x³+x²+x+1). @=e2ri/5 then w²+w³+w²+w+1=0. COS

Deduce that if (b) Let a 2 cos 2 and ß = 2 cos 4. Show that a = @ +w4 and B=w² +0³. Find a quadratic equation with roots a,ß. Hence show that 27=(√5-1). 7. (a) Show that x-1=(x-1)(x²+x³+x²+x+1). @=e2ri/5 then w²+w³+w²+w+1=0. COS

Advanced Engineering Mathematics
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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Question
- 7. (a) Show that x − 1 = (x − 1)(x² + x³+x²+x+1). Deduce that if @=e²i/5 then w4+w³+w²+w+1=0. (b) Let a = = 2 cos 2 and ß = 2 cos 4. Show that a = @ + 04 and ß = ²+w³. Find a quadratic equation with roots a,ß. Hence show that =(√5-1). COS 2π 5
Transcribed Image Text:- 7. (a) Show that x − 1 = (x − 1)(x² + x³+x²+x+1). Deduce that if @=e²i/5 then w4+w³+w²+w+1=0. (b) Let a = = 2 cos 2 and ß = 2 cos 4. Show that a = @ + 04 and ß = ²+w³. Find a quadratic equation with roots a,ß. Hence show that =(√5-1). COS 2π 5
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