- #1

chwala

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## Homework Statement:

- find the square root of ## a+b+√(2ab +b^2)##

## Relevant Equations:

- square root

find the square root of ## a+b+√(2ab +b^2)##

let ##√[a+b+√(2ab +b^2)]= ±(√x +√y)##

then, ##a+b+√(2ab +b^2)= x+y+ 2√(xy)##

where ##a+b=x+y##....................................1

##(b+a)^2-a^2=4xy## .....................2

from 2,

##a^2=(b+a)^2-4xy##

##a=√[x+y)^2-4xy]##

##a=√[x^2-2xy+y^2]##

##a=x-y##

therefore,

##b=x+y-x+y##

##b=2y##

##y=\frac {b}{2}##

→##x=a+\frac {b}{2}##

this is my original working...i am looking for any alternative method?

let ##√[a+b+√(2ab +b^2)]= ±(√x +√y)##

then, ##a+b+√(2ab +b^2)= x+y+ 2√(xy)##

where ##a+b=x+y##....................................1

##(b+a)^2-a^2=4xy## .....................2

from 2,

##a^2=(b+a)^2-4xy##

##a=√[x+y)^2-4xy]##

##a=√[x^2-2xy+y^2]##

##a=x-y##

therefore,

##b=x+y-x+y##

##b=2y##

##y=\frac {b}{2}##

→##x=a+\frac {b}{2}##

this is my original working...i am looking for any alternative method?