Which of the following is b equal to in terms of a if a 0 and 4/b

Question

Which of the following is b equal to in terms of a if a> 0 and 4/b = a/5 + 5/a?

a) 20a/(a^2 + 25)
b) 5a/(a^2 + 25)
c) 20/(a^2 +25)
d) (a^2 +25)/(20a)
e) (20a +5)/(a^2 + 25a)

Bunuel · Answer

\frac{4}{b} = \frac{a}{5} + \frac{5}{a} ;

\frac{4}{b} = \frac{a^2+25}{5a} ;

20a=b(a^2+25) ;

b= \frac{20a}{a^2+25} .

Answer: A.

Kinshook · Answer

Asked: Which of the following is b equal to in terms of a if a> 0 and 4/b = a/5 + 5/a?

4/b = a/5 + 5/a
4/b = (a^2 + 25)/5a
1/b = (a^2 + 25)/20a
b = 20a/(a^2 + 25)

IMO A

globaldesi · Answer

Solve the equation
 \frac{4}{b} = \frac{a^2+5b}{5a} 
or 
 \frac{1}{b} = \frac{a^2+5b}{20a} 
divide entire side by 1
 b = \frac{20a}{a^2 +5b} 
thus A

hiranmay · Answer

Which of the following is b equal to in terms of a if a> 0 and 4/b = a/5 + 5/a?

a) 20a/(a^2 + 25) -->   correct : 4/b = a/5 + 5/a = (a^2+25)/5a => b = 20a/(a^2+25) 
b) 5a/(a^2 + 25)
c) 20/(a^2 +25)
d) (a^2 +25)/(20a)
e) (20a +5)/(a^2 + 25a

Which of the following is b equal to in terms of a if a> 0 and 4/b

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