(i) `(sqrt2 -1)/(sqrt2 + 1) =a+bsqrt2`

log((sqrt2-1)/(sqrt2+1))

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)

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

In each of the following determine rational number a\ a n d\ b : (i)\ (3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2) (ii)\ (5+3sqrt(3))/(7+4sqrt(3))=a+bsqrt(3)

Find the value of a and b if (i)(sqrt(3)+1)/(sqrt(3)-1)=a+bsqrt(3)" "(ii)(5+2sqrt(3))/(5-2sqrt(3))=a+bsqrt(3)

If the point P(a ,a^2) lies completely inside the triangle formed by the lines x=0,y=0, and x+y=2, then find the exhaustive range of values of a is (A) (0,1) (B) (1,sqrt2) (C) (sqrt2 -1,1) (D) (sqrt2 -1,2)

The sum of (1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/( 4 sqrt3 + 3 sqrt4 ) +...+(1)/( 25 sqrt 24 + 24 sqrt25) is

If alpha, betaepsilon(0, pi/2) and if sin^4alpha+4cos^4beta+2=4sqrt2 sinalphacosbeta then the value of cos(alpha+beta)-cos(alpha-beta) is (A) sqrt2 (B) 1/sqrt2 (C) -1/sqrt2 (D) -sqrt2

Let a,b inQ"such that"(39sqrt2-5)/(3-sqrt2)=a+bsqrt2, then (A) sqrt((b)/(a)) is a rational number (B) b and a are coprime rational numbers (C) b-a is a composite number (D) sqrt(a+b) is a rational number

For the following sequence in G.P. find the sum of infinite terms. " " (sqrt2+1)/(sqrt2-1) +(1)/(2-sqrt2)+ (1)/(2)+ ………………