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If (x – y) = and (x + y) = , what is the value of x2 – y2

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

If (x – y) = and (x + y) = , what is the value of x2 – y2 [#permalink]  17 Jul 2018, 11:50
Expert's post
00:00

Question Stats:

60% (00:08) correct 40% (01:01) wrong based on 10 sessions
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.
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

Re: If (x – y) = and (x + y) = , what is the value of x2 – y2? ( [#permalink]  18 Jul 2018, 07:16
Expert's post
Explanation

The factored form of the Difference of Squares (one of the “special products” you need to memorize for the exam) is comprised of the terms given in this problem:
$$x^2 - y^2 = (x + y)(x - y)$$

Substitute the values $$\sqrt{12}$$ and $$\sqrt{3}$$ in place of (x – y) and (x + y), respectively:

x^2 - y^2 = $$\sqrt{12} \times \sqrt{3}$$

Combine 12 and 3 under the same root sign and solve:
$$x^2 - y^2 =\sqrt{12} \times \sqrt{3}$$
$$x^2 - y^2 =\sqrt{36}$$
$$x^2 - y^2 = 6$$
_________________

Sandy
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Re: If (x – y) = and (x + y) = , what is the value of x2 – y2? (   [#permalink] 18 Jul 2018, 07:16
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