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05 Jun 2023, 10:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
63% (02:17) correct
37%
(02:31)
wrong
based on 350
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If \(x^2 + 10y^2 - 6xy – 2y + 1 = 0\), what is the value of \(x\)?
\(A. 0\)
\(B. 1\)
\(C. 2\)
\(D. 3\)
\(E. 4\)
\(A. 0\)
\(B. 1\)
\(C. 2\)
\(D. 3\)
\(E. 4\)
08 Jun 2023, 10:16
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Bunuel
\(x^2+9y^2+y^2-2.3xy-2y+1=0 \)
\((x-3y)^2 + (y-1)^2= 0\)
We know both \(x-3y\) and \(y-1\) should be equal to \(0\) for the eqn. to hold.
Hence \(y = 1\)
Therefore \(x-3y = 0\)
\(x-3 = 0\) ( Putting \(y=1\) )
\(x=3 \)
Ans D
Hope it helps.
General Discussion
15 Jun 2024, 02:37
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Instead of solving algebraically, I did it by substituting values of x.
For x = 0, 10y^2 -2y+1 = 0 does not have any real roots.
For x = 1, 10y^2 - 8y + 2 = 0 does not have any real roots.
For x = 2, 10y^2 - 14y + 5 = 0 does not have any real roots.
For x = 3, 10y^2 - 20y + 10 = 0 has real roots and can be solved. This should be the answer but lets check the last option as well.
For x = 4, 10y^2 - 26y + 17 = 0 does not have any real roots.
Answer: D, x = 3
For x = 0, 10y^2 -2y+1 = 0 does not have any real roots.
For x = 1, 10y^2 - 8y + 2 = 0 does not have any real roots.
For x = 2, 10y^2 - 14y + 5 = 0 does not have any real roots.
For x = 3, 10y^2 - 20y + 10 = 0 has real roots and can be solved. This should be the answer but lets check the last option as well.
For x = 4, 10y^2 - 26y + 17 = 0 does not have any real roots.
Answer: D, x = 3
