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If a+b=x and a-b= y

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If a+b=x and a-b= y  [#permalink]

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New post 09 Aug 2017, 08:36
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

82% (01:28) correct 18% (02:43) wrong based on 73 sessions

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If a+b=x and a-b= y , then 2ab=?

A. (x^2-y^2)/2
B. (y^2-x^2)/2
C. x-y/2
D. 2xy
E. (x^2+y^2)/2

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Re: If a+b=x and a-b= y  [#permalink]

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New post 09 Aug 2017, 09:06
1
Given:
a+b=x -> (1)
a-b= y -> (2)

(1)+(2) => \(x+y = 2a\) ->(3)
(1)-(2) => \(x-y = 2b\) ->(4)

Multplying (3) and (4),we get
\(4ab = (x-y)(x+y) = x^2 - y^2\)

Therefore, \(2ab = \frac{x^2 - y^2}{2}\)(Option A)
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Re: If a+b=x and a-b= y  [#permalink]

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New post 09 Aug 2017, 10:45
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Re: If a+b=x and a-b= y  [#permalink]

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New post 09 Aug 2017, 11:49
a+b=x (1); a-b=y (2) adding 1&2 a=x+y/2
substituting a in 1; b= x-y/2: Plug in values of a and b in 2ab=x^2-y^2/2
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Re: If a+b=x and a-b= y  [#permalink]

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New post 10 Aug 2017, 03:31
Skywalker18 wrote:
If a+b=x and a-b= y , then 2ab=?

A. (x^2-y^2)/2
B. (y^2-x^2)/2
C. x-y/2
D. 2xy
E. (x^2+y^2)/2



Let a = 2 & b=1 then x = 3 & y = 1.............2ab = 4

We search which value from below equation will give 4

A. (x^2-y^2)/2 = (9 - 1)/2 = 4.......................Keep

B. (y^2-x^2)/2...No need for calculation will give negative........Eliminate

C. (x-y)/2 = 1/2..........Eliminate

D. 2xy = 6..................Eliminate

(x^2+y^2)/2 = 5........Eliminate

Answer: A
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Re: If a+b=x and a-b= y  [#permalink]

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New post 14 Aug 2017, 15:10
Skywalker18 wrote:
If a+b=x and a-b= y , then 2ab=?

A. (x^2-y^2)/2
B. (y^2-x^2)/2
C. x-y/2
D. 2xy
E. (x^2+y^2)/2


We can square each equation:

(a + b)^2 = x^2

a^2 + b^2 + 2ab = x^2 [Eq. 1]

and

(a - b)^2 = y^2

a^2 + b^2 - 2ab = y^2 [Eq. 2]

Now if we subtract Eq. 2 from Eq. 1, we have:

4ab = x^2 - y^2

2ab = (x^2 - y^2)/2

Alternative solution:

We are given that a + b = x and a - b = y. If we add the two equations, we have 2a = x + y or a = (x + y)/2. Similarly, if we subtract the two equations, we have 2b = x - y or b = (x - y)/2. Thus:

2ab = 2 * (x + y)/2 * (x - y)/2 = (x + y)(x - y)/2 = (x^2 - y^2)/2

Answer: A
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Re: If a+b=x and a-b= y   [#permalink] 14 Aug 2017, 15:10
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