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If xy=1

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by amising6 » Wed Jun 16, 2010 5:43 pm
xy =1
(2^(x+y)^2)/(2^(x-Y)^2)

now we will use one concept which say that a^b/a^c=a^(b-c)
so we can reduce the given problem to 2 ^(((x+y)^2)-((x-y)^2))
2^(x^2+y^2+2xy -(x^2+y^2 - 2xy)) as we know (a+b)^2=a^2+b^2+2ab and (a-b)^2=a^2+b^2-2ab
2^(4xy) since remaining term will cancel out
2^(4*1)
2^4=16
Ideation without execution is delusion
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by ssuarezo » Wed Jun 16, 2010 5:51 pm
amising6 wrote:xy =1
(2^(x+y)^2)/(2^(x-Y)^2)

now we will use one concept which say that a^b/a^c=a^(b-c)
so we can reduce the given problem to 2 ^(((x+y)^2)-((x-y)^2))
2^(x^2+y^2+2xy -(x^2+y^2 - 2xy)) as we know (a+b)^2=a^2+b^2+2ab and (a-b)^2=a^2+b^2-2ab
2^(4xy) since remaining term will cancel out
2^(4*1)
2^4=16
Thanks Amising6
Actually, I knew the rule, but I dont' know why I get blocked during the exam with a timer !!.
Silvia
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