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If both `a and b` are rational numbers, find the values of `a and b` in each of the following equalities:Given, `(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1)=a+bsqrt3`

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Given,`(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1)`
`=> (sqrt(3)-1)^2/2`
`=>2-sqrt(3)`
`=>2-sqrt(3)=a+b sqrt(3)`
`=>a=2 ,b=-1`
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RD SHARMA-RATIONALISATION -All Questions
  1. Simplify each of the following by rationalising the denominator: 1/(...

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  2. Simplify each of the following by rationalizing the denominator: I(I...

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  3. If both a and b are rational numbers, find the values of a and b in e...

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  4. If both a\ a n d\ b are rational numbers, find the values of a\ a n d\...

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  5. If both a and b are rational numbers, find the values of a and b in ea...

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  6. If both a\ a n d\ b are rational numbers, find the values of a\ a n d\...

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  7. If both a\ a n d\ b are rational numbers, find the values of a\ a n d\...

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  8. If both a\ a n d\ b are rational numbers, find the values of a\ a n d\...

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  9. If both a\ a n d\ b are rational numbers, find the values of a\ a n d\...

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  10. Simplify : 3/(5-sqrt(3))+2/(5+\ sqrt(3))

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  11. Simplify: (4+\ sqrt(5))/(4-sqrt(5))+(4-\ sqrt(5))/(4+\ sqrt(5))

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  12. Simplify: (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+\ 2)/(sqrt(5)-\ 2)

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  13. Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-...

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  14. Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/...

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  15. If x=2+sqrt(3) , find the value of x^2+1/(x^3)

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  16. If x=3-2sqrt(2),find x^2+1/(x^2)

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  17. If x=1-sqrt(2) , find the value of (x-1/x)^3

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  18. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

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  19. If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b...

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  20. If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

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