5. Show that: b>0 and a <0 such that a² = b⇒a= -√b. 6. Prove that there are real numbers a and b, such that (a + b)² = a² + b²
5. Show that: b>0 and a <0 such that a² = b⇒a= -√b. 6. Prove that there are real numbers a and b, such that (a + b)² = a² + b²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%

Transcribed Image Text:段階的に解決し、人工知能を使用せず、 優れた仕事を行います
ご支援ありがとうございました
SOLVE STEP BY STEP IN DIGITAL FORMAT
DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI |
5. Show that:
b>0 and a < 0 such that a² = b ⇒a=-√b.
6. Prove that there are real numbers a and b, such that
(a+b)2 = a²+62
Expert Solution

Step 1: Solution of 5
We are given that b>0 and a<0
Now, let a2 = b
Taking square root on both sides, we get,
a = ±√b
As a<0, we take the negative sign.
So, a = -√b
Conversely, if a = -√b, then squaring both sides, we get
a2 = (-√b)(-√b) = +(√b)2 = b
Hence, proved.
Step by step
Solved in 3 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

