2. We are trying to prove the inequality (alb1 + a2b2 + .. + anbn) s (af + ak+ .. + an)(bf + b3 + ..+ bh) for all ak, bk ER, 1 0. Determine the precise conditions on A, B.C under which g(x) 2 0 for all x. • Define f: R R by S(x) = (alx + b1)²+ (a2x + b2)2 + .. + (apx + bn)?. Write f in the form f(x) = Ax+ Bx + C, with A, B and C expressed in terms of ak, bk-
2. We are trying to prove the inequality (alb1 + a2b2 + .. + anbn) s (af + ak+ .. + an)(bf + b3 + ..+ bh) for all ak, bk ER, 1 0. Determine the precise conditions on A, B.C under which g(x) 2 0 for all x. • Define f: R R by S(x) = (alx + b1)²+ (a2x + b2)2 + .. + (apx + bn)?. Write f in the form f(x) = Ax+ Bx + C, with A, B and C expressed in terms of ak, bk-
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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How would you prove this?
![2. We are trying to prove the inequality
(alb1+ a2b2+
- + anbn < (a}+ az+ . + an)(b}+ b3+ ...+ b)
.* + ah)(b} + b3+ .. + bh)
for all ak, bk ER, 1 < k < n.
» Let g : R -R be given by g(x) = Ax+ Bx + C where A, B, C E R with A > 0. Determine the precise conditions on A, B, C under which g(x) > 0 for all x.
• Define f : R → R by
f(x) = (a]x+ b1)-+(a2x + b2)² +
..- + (anx + bn)².
Write f in the form f(x) = Ax+ Bx + C, with A, B and C expressed in terms of ak, bk.
Use parts (a) and (b) to prove the inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66318fc8-0ad6-4ce3-b166-594a4cfc43a5%2F13fe2524-9cb1-4771-a60c-1e88af96e63e%2Fokv904i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. We are trying to prove the inequality
(alb1+ a2b2+
- + anbn < (a}+ az+ . + an)(b}+ b3+ ...+ b)
.* + ah)(b} + b3+ .. + bh)
for all ak, bk ER, 1 < k < n.
» Let g : R -R be given by g(x) = Ax+ Bx + C where A, B, C E R with A > 0. Determine the precise conditions on A, B, C under which g(x) > 0 for all x.
• Define f : R → R by
f(x) = (a]x+ b1)-+(a2x + b2)² +
..- + (anx + bn)².
Write f in the form f(x) = Ax+ Bx + C, with A, B and C expressed in terms of ak, bk.
Use parts (a) and (b) to prove the inequality.
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