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In each of the following determine ratio...

In each of the following determine rational number `a and b :` `(sqrt(3)-1)/(sqrt(3)+1)=a-bsqrt(3)` (ii) `(4+ sqrt(2))/(2+sqrt(2))=a-sqrt(b)`

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`(sqrt(3)-1)/(sqrt(3)+1)=((sqrt(3)-1)\(sqrt(3)-1))/((sqrt(3)+1)\(sqrt(3)-1))`
Rationalising the denominator
`=(sqrt(3)-1)^2/((sqrt(3))^2-(1)^2)`
`=(3+1-2sqrt(3))/(3-1)`
`=(4-2sqrt(3))/2`
`=2-sqrt3`
Therefore,
`2-sqrt3=a-bsqrt(3)`
Comparing, we get
`a=2, b=1`

(ii) `((4+sqrt(2))\(2-sqrt(2)))/((2+ sqrt(2))\(2-sqrt(2))`
`=(4(2-sqrt(2))+sqrt(2)\(2-sqrt(2)))/((2)^2-(sqrt(2)^2))`
`=(8-4sqrt(2)+2sqrt(2)-2)/(4-2)`
`=(6-2sqrt(2))/2`
Therefore,
`3-sqrt(2)=a-sqrt(b)`
Comparing, we get
`a=3 and b=2`
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