If a is rational and b is irrational, show that :
`(a)/(b)[a != 0]` cannot be rational.

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.

If f(x)={x ,x is rational 1-x ,x is irrational ,then f(f(x)) is

Show that the sum of a rational number and an irrational number cannot be rational.

If x, y are rationals and xsqrt(2) - ysqrt(3) = 0 , show that x = y = 0

IF a,b,c are rational and a+b+c=0, show that the roots of the equation ax^2+bx+c=0 are rational.

Give four examples for rational and irrational numbers?

The number of rational point(s) [a point (a, b) is called rational, if aa n db both are rational numbers] on the circumference of a circle having center (pi,e) is (a)at most one (b) at least two (c)exactly two (d) infinite

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={(0, x in rational) (x ,x in irrational) and g(x)={(O, x in irrational x), (x in rational) then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

By taking two examples of irrational numbers prove that (a) the sum of them is a rational number, (b) the product of them is a rational number.