33. V2m – 1+2= m-34. V2x + 9 = Va +3%3|35. Vē+ V1– e = 1

The equation is 2m-1+2=m. Find the value of m: 2m-1=m-22m-12=m-222m-1=m2-4m+4m2-6m+5=0 Solve the…

Answered: 33. V2m – 1+2= m - 34. V2x + 9 = Va +3…

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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33. V2m – 1+2= m
-
34. V2x + 9 = Va +3
%3|
35. Vē+ V1– e = 1

Expert Solution

Solution 33:

The equation is $\sqrt{2 m - 1} + 2 = m$ .

Find the value of m:

$\sqrt{2 m - 1} = m - 2 {(\sqrt{2 m - 1})}^{2} = {(m - 2)}^{2} 2 m - 1 = m^{2} - 4 m + 4 m^{2} - 6 m + 5 = 0$

Solve the quadratic equation:

$m^{2} - 5 m - m + 5 = 0 m (m - 5) - (m - 5) = 0 (m - 5) (m - 1) = 0 m = 1, 5$

However, only m = 5 satisfies the equation.

Solution 34:

The equation is $\sqrt{2 x + 9} = \sqrt{x} + 3$ .

Find the value of x:

${(\sqrt{2 x + 9})}^{2} = {(\sqrt{x} + 3)}^{2} (S q u a r e b o t h s i d e s) 2 x + 9 = x + 9 + 6 \sqrt{x} x = 6 \sqrt{x} x^{2} = {(6 \sqrt{x})}^{2} (S q u a r e b o t h s i d e s a g a i n)$

Solve the quadratic equation:

$x^{2} = 36 x x (x - 36) = 0 x = 0 or x = 36$

Here, both x=0, 36 satisfies the equation.

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