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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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17 Jul 2018, 23:46
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Question Stats:

81% (00:35) correct 19% (01:49) wrong based on 42 sessions

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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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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

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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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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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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.

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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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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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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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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

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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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