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If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2

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If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 17 Jul 2018, 23:46
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If \((x - y) =\sqrt{12}\) and \((x + y) = \sqrt{3}\), what is the value of \(x^2 - y^2\)?

(A) 3
(B) 6
(C) 9
(D) 36
(E) It cannot be determined from the information given.

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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 17 Jul 2018, 23:56
Bunuel wrote:
If \((x - y) =\sqrt{12}\) and \((x + y) = \sqrt{3}\), what is the value of \(x^2 - y^2\)?

(A) 3
(B) 6
(C) 9
(D) 36
(E) It cannot be determined from the information given.



Given

\((x - y) =\sqrt{12}\)

\((x + y) = \sqrt{3}\)

\(x^2 - y^2\)

= (x+y) (x-y)

= \(\sqrt{12}\) \(\sqrt{3}\)

= \(\sqrt{36}\)

= 6

The best answer is B.
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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 18 Jul 2018, 00:30
+ for B

= x^2 - y^2
= (x + y) * (x - y)
= √3 * √12
= √36
= 6

Hence, B.
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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 18 Jul 2018, 05:46

Solution



Given:

    • \((x−y)= \sqrt{12}\)
    • \((x+y)=\sqrt{3}\)


To find:
• The value of \(x^2- y^2\).

Approach and Working:

• \(x^2- y^2= (x-y)(x+y)\)
• =\(\sqrt{12}*\sqrt{3}= \sqrt{36}= 6\)

Hence, the correct answer is option B.

Answer: B
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If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 18 Jul 2018, 05:55
√12 * √3 = √12(3) = √36 = 6.

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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 18 Jul 2018, 07:32
Bunuel wrote:
If \((x - y) =\sqrt{12}\) and \((x + y) = \sqrt{3}\), what is the value of \(x^2 - y^2\)?

(A) 3
(B) 6
(C) 9
(D) 36
(E) It cannot be determined from the information given.


\(x^2 - y^2 = (x - y)(x + y)\)

So, \(x^2 - y^2 = \sqrt{12}*\sqrt{3}\)

Or, \(x^2 - y^2 = \sqrt{36}\)

Thus, \(x^2 - y^2 = 6\), Answer must be (B)

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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2  [#permalink]

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New post 22 Jul 2018, 18:13
Bunuel wrote:
If \((x - y) =\sqrt{12}\) and \((x + y) = \sqrt{3}\), what is the value of \(x^2 - y^2\)?

(A) 3
(B) 6
(C) 9
(D) 36
(E) It cannot be determined from the information given.


Let’s first factor the expression x^2 - y^2 and then substitute with the given values:

x^2 - y^2 = (x - y)(x + y) = (√12)(√3) = √36 = 6

Answer: B
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Re: If (x - y) = 12^(1/2) and (x + y) = 3^(1/2), what is the value of x^2 &nbs [#permalink] 22 Jul 2018, 18:13
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