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13 Feb 2020, 07:50
Kudos
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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:
25%
(medium)
Question Stats:
79% (01:46) correct
21%
(02:25)
wrong
based on 306
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
A. 20
B. 30
C. 50
D. 60
E. 90
13 Feb 2020, 08:13
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Bookmarks
Bunuel
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of \(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
A. 20
B. 30
C. 50
D. 60
E. 90
Given: \(x + y = 6t\)
Square both sides to get: \((x + y)^2 = (6t)^2\)
Expand and simplify: \(x^2 + 2xy + y^2 = 36t^2\)
Also given: \(xy = -7t^2\)
Multiply both sides by 2 to get: \(2xy = -14t^2\)
We now have two equations:
\(x^2 + 2xy + y^2 = 36t^2\)
\(2xy = -14t^2\)
Subtract the bottom equation from the top equation to get: \(x^2 + y^2 = 50t^2\)
Our goal is to find the value of \(\frac{(x^2 + y^2)}{t^2}\)
Replace the numerator with its equivalent value to get: \(\frac{50t^2}{t^2}\)
Simplify to get: 50
Answer: C
Cheers,
Brent
General Discussion
14 Feb 2020, 08:13
Kudos
Bookmarks
given
\(\frac{(x^2 + y^2)}{t^2}\)
can be re written as ;
\(\frac{(x^2 + y^2+2xy-2xy)}{t^2}\)
\(\frac{(x + y)^2-2xy}{t^2}\)
substitute given function values
we get 50 as answer
IMO C
\(\frac{(x^2 + y^2)}{t^2}\)
can be re written as ;
\(\frac{(x^2 + y^2+2xy-2xy)}{t^2}\)
\(\frac{(x + y)^2-2xy}{t^2}\)
substitute given function values
we get 50 as answer
IMO C
Bunuel
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
A. 20
B. 30
C. 50
D. 60
E. 90
