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Which of the follow is a set of all possible values of y that satisfy

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Alhamdan1995
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Which of the follow is a set of all possible values of y that satisfy [#permalink] New post  16 May 2020, 14:59
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65% (01:38) correct 35% (01:46) wrong based on 153 sessions
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\(y-13\sqrt{y}+36 = 0\)

A) (2,3)
B) (+/-2,+/-3)
C) (4,9)
D) (-4,-9)
E) (16,81)
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chetan2u
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Re: Which of the follow is a set of all possible values of y that satisfy [#permalink] New post  16 May 2020, 20:52
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Alhamdan1995 wrote:
\(y-13\sqrt{y}+36 = 0\)

A) (2,3)
B) (+/-2,+/-3)
C) (4,9)
D) (-4,-9)
E) (16,81)


Choices


Since we have \(\sqrt{y}\), y cannot be negative, so you can straight way eliminate the choices B and D.
A) (2,3)
\(y-13\sqrt{y}+36 = 0\) => \(2-13\sqrt{2}+36 = 0\)..NO
B) (4,6)
\(y-13\sqrt{y}+36 = 0\) => \(4-13\sqrt{4}+36 = 0.....40-26=0\)..NO
C) (16,81)
\(y-13\sqrt{y}+36 = 0\) => \(16-13\sqrt{16}+36 = 0....42-13*4=0\)..YES

Algebraic


Let \(\sqrt{y}=x..\)
So, \(x^2-13x+36=0...(x-4)(x-9)=36\)
But, remember we are looking for y, and \(y=x^2...so y=4^2=16....y=9^2=36\)

E
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Which of the follow is a set of all possible values of y that satisfy [#permalink] New post  17 May 2020, 08:13
Alhamdan1995 wrote:
\(y-13\sqrt{y}+36 = 0\)

A) (2,3)
B) (+/-2,+/-3)
C) (4,9)
D) (-4,-9)
E) (16,81)


\(y-13\sqrt{y}+36 = 0\)

Let \(\sqrt{y}\) be x; y=x^2

\(x^2 - 13x + 36 = 0\)
\(x^2 - 9x - 4x + 36 = 0\)
(x-9)(x-4)=0
x = 9 or x = 4
If x=9; \(\sqrt{y} = 9; y=81\)
If x=4; \(\sqrt{y} = 4; y=16\)

IMO E
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Re: Which of the follow is a set of all possible values of y that satisfy [#permalink] New post  17 May 2020, 14:01
Alhamdan1995 wrote:
\(y-13\sqrt{y}+36 = 0\)

A) (2,3)
B) (+/-2,+/-3)
C) (4,9)
D) (-4,-9)
E) (16,81)


\(y−13\sqrt{y}+36=0\)

Let \(\sqrt{y} = x\) => \(y=x^2\)

\(x^2−13x+36=0\)
(x-9)(x-4)=0
x = 9 or x = 4

Therefore,
[m]\sqrt{y} = 9 => y = 81
[m]\sqrt{y} = 4 => y = 16

y = 16,81

Answer - E
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v12345
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Re: Which of the follow is a set of all possible values of y that satisfy [#permalink] New post  15 Sep 2021, 08:08
Alhamdan1995 wrote:
\(y-13\sqrt{y}+36 = 0\)

A) (2,3)
B) (+/-2,+/-3)
C) (4,9)
D) (-4,-9)
E) (16,81)


\(y-13\sqrt{y}+36 = 0\)
\(\sqrt{y} \)=4 or 9
y = 16 or 81
Hence, OA is (E).
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Re: Which of the follow is a set of all possible values of y that satisfy [#permalink]
15 Sep 2021, 08:08
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