" (ii) "[(1+3sqrt(2)x)^(7)+(1-3sqrt(2)x)^(7)]

Rationalise the denominator of each of the following. (i) (1)/(sqrt(7)) (ii) (sqrt(5))/(2sqrt(3)) (iii) (1)/(2+ sqrt(3)) (1)/(sqrt(3)) (v) (1)/((5+3sqrt(2)) (vi) (1)/(sqrt(7) - sqrt(6)) (vi) (1)/(sqrt(7) - sqrt(6)) (viii) (1+ sqrt(2))/(2-sqrt(2)) (ix) (3-2sqrt(2))/(3+2sqrt(2))

Simplify : (x+sqrt(x^(2)-1))^(7) + (x-sqrt(x^(2)-1))^(7)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

lim_(x rarr sqrt(2))(x^(2)-3sqrt(2)x+4)/(x^(3)+7x-9sqrt(2))

sqrt(3x^(2)-7x-30)-sqrt(2x^(2)-7x-5)=x-5

If n be the degree of the polynomial sqrt(3x^(2)+1){(x+sqrt(3x^(2)+1))^(7)-(x-sqrt(3x^(2)+1))^(7)} then n is divisible by

The expression (1)/( sqrt( 3x +1)) [ ( ( 1+ sqrt( 3x + 1))/(2))^(7) - (( 1- sqrt ( 3x +1))/(2))^(7)] is a polynomial in x of degree eual to

If 0

If x=(7+5sqrt(2))^(1/3) -1/((7+5sqrt(2))^(1/3) , then the value of x^3+3x-14 is equal to 1 (b) 0 (c) 2 (d) 4