Class 9th math exercise 1f Rs aggarwal

 Class 9th math exercise 1f Question 1

1.Write the rationalising factor of the denominator in 1/(√2+√3)

Solution:- The rationalising factor of the denominator in 1/(√2+√3) is √2-√3

Explanation:- 

The rationalising factor of √a+√b is √a-√b

and The rationalising factor of √a-√b is √a+√b

Class 9th math exercise 1f Question 11

Q. 11 if x=3+2√2 check whether x+1/x is rational or irrational

Solution:- 

Class 9th math exercise 1f Question 12

12. If x=2-√3 , find the value of (x-1/x)³.

Solution:- Given x=2-√3

Then 1/x=1/2-√3=1×(2+√3)/(2-√3)(2+√3) 

=(2+√3)/{2²-(√3)²}

=(2+√3)/(4-3) 

=(2+√3)/1

=2+√3

Now (x-1/x)³={(2-√3-(2+√3)}³

={2-√3-2-√3}³

=(-2√3)³

=-8×3√3

=-24√3

Class 9th math exercise 1f Question 13

13. If x=9-4√5 , find the value of x²+1/x².

Solution:- Given x=9-4√5

Then 1/x=1/9-4√5=1×(9+4√5)/(9-4√5)(9+4√5) 

=(9+4√5)/{9²-(4√5)²}

=(9+4√5)/(81-80) 

=(9+4√5)/1

=9+4√5

Now x²+(1/x²)={x+(1/x)}²-2×x×1/x

={x+(1/x)}²-2

=(9-4√5+9+4√5)²-2

=(9+9)²-2

=(18)²-2

=324-2

=322