Let a, b, c, d be positive rationals such that `a+sqrtb=c+sqrtd`, then either a = c and b = d or b and d are squares of rationals.

Let a, b, c, d be positive integers such that log_(a) b = 3//2 and log_(c) d = 5//4 . If (a-c) = 9, then find the value of (b-d).

If a, b, c and d are four positive real numbers such that sum of a, b and c is even the sum of b,c and d is odd, then a^2-d^2 is necessarily

Let a,b,c,d,e, be real numbers such that a+b lt c+d , b+c lt d+e, c+d lt e+a, d+e lt a+b . Then

Let a , b , c , d are positive integer such that log_(a)b=3//2 and log_(c)d=5//4 . If a-c=9 , then value of (b-d) is equal to

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

If a,b,c are positive rational numbers such that agtbgtc and the quadratic eqution (a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 has a root of the interval (-1,0) then (A) c+alt2b (B) the roots of the equation are rational (C) the roots of are imaginary (D) none of these

Let a, b, c, d, e be natural numbers in an arithmetic progression such that a + b + c + d + e is the cube of an integer and b + c + d is square of an integer. The least possible value of the number of digits of c is