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02 Mar 2020, 06:26
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If \(x\) is a positive number and \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\), where the given expression extends to an infinite number of roots, then what is the value of \(x\)?
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
02 Mar 2020, 06:30
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Bunuel
If \(x\) is a positive number and \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\), where the given expression extends to an infinite number of roots, then what is the value of \(x\)?
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
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Hope it helps.
02 Mar 2020, 06:35
Kudos
Bookmarks
Bunuel
If \(x\) is a positive number and \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\), where the given expression extends to an infinite number of roots, then what is the value of \(x\)?
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
What we have is \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\)
Squaring both sides
\(x+\)\({\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=100\)
But \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}\) on left side after the first x+ is same as given in question which has given va;ue i.e. 10 therefore
\(x+\)10\(=100\)
\({x}=90\)
Answer: Option B
