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# If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =

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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
Bunuel wrote:
If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =

A. 0
B. 5
C. 10
D. 15
E. 20

Hi
if x ¤ y = (x + y)^2 - (x - y)^2 then √5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2
let solve the equation:
$$√5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2$$
$$=>√5 ¤ √5 = (√5+√5)^2$$
$$=>√5 ¤ √5 = (√5)^2 + 2 * √5 * √5 +(√5)^2$$
$$=>√5 ¤ √5 = 5 + 2 * 5 + 5$$
$$=>√5 ¤ √5 = 5+10+5$$
$$=>√5 ¤ √5 = 10+10$$
$$=>√5 ¤ √5 = 20$$

Originally posted by HungNguyen on 13 May 2016, 06:46.
Last edited by HungNguyen on 13 May 2016, 06:48, edited 1 time in total.
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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
(x + y)^2 - (x - y)^2 = 4xy

√5 ¤ √5 = 4*5 = 20

OA : E
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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
More than anything - Here it pays to first understand what the function actually does.

x ¤ y simply means - $$(Sum\ of\ x \ and \ y)^2 - (difference \ of \ x \ and \ y)^2$$

Given $$x=y=\sqrt{5}$$.

Therefore (Sum of x and y) = $$2\sqrt{2}$$. (Difference of x and y) = 0

WIth Minimum calculation required answer = $$(2\sqrt{5})^2 = 20$$.

Aside Moderators: Do you think it will be nice'er' if the stem is made math friendly?
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
$$If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =$$

Another way to simplify is to realize that this is a difference of squares pattern. Really, it's a difference of two terms pattern if I can call it that.

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

So, you can spell it out but if you realize, the first terms are positive when factoring, and the second set of terms has just one negative. You'll really end up with $$(2*\sqrt{5})$$ $$(2*\sqrt{5})$$
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
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