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If (x+5) (1/x+1/5)=4, then x=
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05 Apr 2019, 05:02
05 Apr 2019, 05:02
Expert Reply
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Question Stats:
90% (01:23) correct
9% (02:15) wrong based on 11 sessions
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If \((x+5) (\frac{1}{x}+\frac{1}{5})=4\), then x=
A. \(\frac{1}{5}\)
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
A. \(\frac{1}{5}\)
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (x+5) (1/x+1/5)=4, then x=
[#permalink]
05 Apr 2019, 06:49
05 Apr 2019, 06:49
1
Carcass wrote:
If \((x+5) (\frac{1}{x}+\frac{1}{5})=4\), then x=
A. \(\frac{1}{5}\)
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
A. \(\frac{1}{5}\)
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
Given: \((x+5) (\frac{1}{x}+\frac{1}{5})=5\)
Use FOIL to expand: x/x + x/5 + x/5 + 5/5 = 4
Simplify: 1 + x/5 + 5/x + 1 = 4
Simplify: x/5 + 5/x + 2 = 4
So: x/5 + 5/x = 2
Multiply both sides by x to get: x²/5 + 5 = 2x
Multiply both sides by 5 to get: x² + 25 = 10x
Rearrange to get: x² - 10x + 25 = 0
Factor: (x - 5)(x - 5) = 0
So, x = 5
Answer: D
Cheers,
Brent
Re: If (x+5) (1/x+1/5)=4, then x=
[#permalink]
06 Apr 2019, 19:48
06 Apr 2019, 19:48
1
PLugging in options is another approach. In this case better will be to start from middle, option C
