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08 Jan 2021, 07:43
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
62% (02:49) correct
38%
(02:51)
wrong
based on 86
sessions
History
Date
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Not Attempted Yet
If \(\sqrt{x+2} + \sqrt{x+8} = 10\), what is the value of \(x+ \frac{191}{100}\)?
(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
08 Jan 2021, 12:40
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\(\sqrt{x+2} + \sqrt{x+8} = 10\)
\(\sqrt{x+8} = 10-\sqrt{x+2} \)
Squaring both sides
\(x+8 = 100+x+2-20\sqrt{x+2}\)
\(20\sqrt{x+2}= 94\)
Squaring both sides
x+2 = (47/10)^2
x= (4.7)^2 -2
x+1.91 = 22.09 -2+1.91=22
\(\sqrt{x+8} = 10-\sqrt{x+2} \)
Squaring both sides
\(x+8 = 100+x+2-20\sqrt{x+2}\)
\(20\sqrt{x+2}= 94\)
Squaring both sides
x+2 = (47/10)^2
x= (4.7)^2 -2
x+1.91 = 22.09 -2+1.91=22
Bunuel
If \(\sqrt{x+2} + \sqrt{x+8} = 10\), what is the value of \(x+ \frac{191}{100}\)?
(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
19 Jan 2021, 10:17
Kudos
Bookmarks
Bunuel
If \(\sqrt{x+2} + \sqrt{x+8} = 10\), what is the value of \(x+ \frac{191}{100}\)?
(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
Solution:(A) 26
(B) 25
(C) 22
(D) 20
(E) 18
Squaring both sides of the equation, we have:
x + 2 + x + 8 + 2√[(x + 2)(x + 8)] = 100
2x + 2√(x^2 + 10x + 16) = 90
√(x^2 + 10x + 16) = 45 - x
Squaring both sides again, we have:
x^2 + 10x + 16 = 2025 - 90x + x^2
100x = 2009
x = 2009/100
Therefore, x + 191/100 = 2009/100 + 191/100 = 2200/100 = 22.
Answer: C
