Prove the statement, Please show all work. 6. There are real numbers a and b such that√a+b = √a+√b.

Answered: Image /qna-images/answer/cdc4f4ea-6063-4e95-b515-23804e11a624.jpg

Answered: √a +b = √a+√b.

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

Prove the statement, Please show all work.

6. There are real numbers a and b such that
√a+b = √a+√b.

Expert Solution

Step 1: Solving this equation

$square root of a plus b end root equals square root of a plus square root of b rightwards double arrow left parenthesis square root of a plus b end root right parenthesis squared equals left parenthesis square root of a plus square root of b right parenthesis squared rightwards double arrow a plus b equals a plus b plus 2 square root of a b end root rightwards double arrow square root of a b end root equals 0 rightwards double arrow left parenthesis square root of a b end root right parenthesis squared equals 0 rightwards double arrow a b equals 0 e i t h e r space a equals 0 space o r space b equals 0$