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If a and b are different integers and |a| = square_root ab

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Jamil1992Mehedi
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If a and b are different integers and |a| = square_root ab [#permalink] New post   24 Apr 2018, 09:51
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If \(a\) and \(b\) are different integers and \(|a|=\sqrt{ab}\) which of the following must be true?

1. \(a=b\)
2. \(a=-b\)
3. \(a=0\)

A. 1 and 2
B. 1 and 3
C. 1 only
D. 2 only
E. 3 only
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E
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Re: If a and b are different integers and |a| = square_root ab [#permalink] New post   24 Apr 2018, 10:00
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Jamil1992Mehedi wrote:
if \(a\) and \(b\) are different integers and \(|a|\)=\(\sqrt{ab}\) which of the following must be true?

1. \(a=b\)
2. \(a=-b\)
3. \(a=0\)

a. 1 and 2
b. 1 and 3
c. 1 only
d. 2 only
e. 3 only

Need solution with proper logical explanation


\(|a|\)=\(\sqrt{ab}\), Square both sides

\(a^2=ab=> a^2-ab=0\)

\(a(a-b)=0\). This implies either \(a=0\) or \(a=b\). but it is given that \(a\) & \(b\) are different integer. Hence \(a=0\)

Option E
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Re: If a and b are different integers and |a| = square_root ab [#permalink] New post   24 Apr 2018, 11:00
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Another approach:
1.Since a and b are different integers. a can't be qual to b. Eliminate statement 1.
2.If a = -b, then a*b = -b^2 (negative) for which square root of ab is not defined, if both are not equal to 0. Eliminate statement 2.
3.Hence a has to be 0.

Answer E.

Jamil1992Mehedi wrote:
if \(a\) and \(b\) are different integers and \(|a|\)=\(\sqrt{ab}\) which of the following must be true?

1. \(a=b\)
2. \(a=-b\)
3. \(a=0\)

a. 1 and 2
b. 1 and 3
c. 1 only
d. 2 only
e. 3 only

Need solution with proper logical explanation
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Re: If a and b are different integers and |a| = square_root ab [#permalink] New post   04 May 2018, 06:05
|a| = square_root ab
test the options that repeats the most
1. a=b (not possible as question says they are different )

eliminate A,B,C options
2. a=−b
3. a=0 (putting zero satisfies the equation )
so eliminate D


a. 1 and 2
b. 1 and 3
c. 1 only
d. 2 only
e. 3 only (answer)
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mysterymanrog
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Re: If a and b are different integers and |a| = square_root ab [#permalink] New post   13 Sep 2023, 14:18
Notice that the absloute value of a and square root of ab must both return a non-negative value.
This implies that a and b must have the same sign, as if they are opposing sign root(ab) will return a non-real value.
Knowing the above and knowing that a and b are different integers, there is only 1 case: where a is 0, and b is any digit.

E
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Re: If a and b are different integers and |a| = square_root ab [#permalink] New post   13 Sep 2023, 16:22
Asked: If \(a\) and \(b\) are different integers and \(|a|=\sqrt{ab}\) which of the following must be true?

a^2 = ab
a^2 - ab = 0
a(a-b) = 0

Either a =0
or
a-b=0 or a=b; Not true since a & b are different integers

a = 0

1. \(a=b\)
If a=0; May not be true
2. \(a=-b\)
May not be true
3. \(a=0\)
Must be true

A. 1 and 2
B. 1 and 3
C. 1 only
D. 2 only
E. 3 only

IMO E
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Re: If a and b are different integers and |a| = square_root ab [#permalink]
13 Sep 2023, 16:22
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