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
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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.
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