1.If x=2+√3 find (x-1/x)³
soln:x=2+√3
1/x=1/2+√3=2-√3
x-1/x=2+√3-(-2-√3)=2√3
(x-1/x)²=(2√3)³=24√3
2.If x=3-2√2 find x²-1/x²
soln:x=3-2√2
x²=(3-2√2)²=17-12√2
1/x²=1/17-12√2=17+12√2
x²-1/x²=17-12√2-(17+12√2)=-24√2
3.rationalise the denominator: 5/3-2√5
soln:5/3-2√5×3+2√5/3+2√5=-15-10√5/11
4.express 0.131313...in the form p/q where p and q are integers and q≠0
soln:let x=0.1313..
100x=13.1313..
100x=13+0.1313
100x=13+x
100x-x=13
99x=13
x=13/99
5.write 4 rational nos btw 1/5 and 2/5
soln:1/5×5/5=5/25
2/5×5/5=10/25
therefore four rational nos btw 1/5 and 2/5 are 6/25,7/25,8/25,9/25
