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Let 7/(2^(1/2) +2^(1/4) +1) = A + B . 2^...

Let `7/(2^(1/2) +2^(1/4) +1) = A + B . 2^(1/4) + C .2^(1/2) + D. 2^(3/4)`, then

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`7/(2^(1/2)+2^(1/4)+1) = A+B*2^(1/4)+C*2^(1/2)+D*2^(3/4)->(1)`
Now, `7/(2^(1/2)+2^(1/4)+1) = 7/(2^(1/2)+2^(1/4)+1) xx ((2^(1/2)+1) - 2^(1/4))/((2^(1/2)+1) - 2^(1/4))`
`= (7((2^(1/2)+1) - 2^(1/4)))/((2^(1/2)+1)^2 - (2^(1/4))^2)`
`=(7(2^(1/2) - 2^(1/4)+1))/(2+1+2(2^(1/2))-2^(1/2)))`
`=(7(2^(1/2) - 2^(1/4)+1))/(3+2^(1/2)) xx (3-2^(1/2))/(3-2^(1/2))`
`=7/7(2^(1/2) - 2^(1/4)+1)(3-2^(1/2))`
`=3*2^(1/2)-3*2^(1/4)+3-2+2^(3/4)-2^(1/2)`
`=1-3*2^(1/4)+2*2^(1/2)+2^(3/4)`
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