6. The condition for the cube of a +ib to be a real number is 1) a=0 or a = + 3b 2) a=0 or b = 13a b=0 or b= 13a 4) b = 0 or a = 1/36

If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+b+c=2, then prove that a/(1-a)b/(1-b)c/(1-c)geq8

Let a ,b ,and c be real numbers such that 4a+2b+c=0 and a b > 0. Then the equation a x^2+b x+c = 0

If a and b are two distinct non-zero real numbers such that a -b =a/b=1/b-1/a, then : (a) a>0 (b) a 0

If a, b are two real number satisfying the relation 2a^(2) - 3a - 1 = 0 and b^(2) + 3b - 2 = 0 and ab ne 1 , then value of (ab + a+ 1)/(b) is

Find the equations of the circles the end points of whose diameter are as follows : (i) (0,6) and (6,0) (ii) (-1,3) and (2,4) (iii) (A+b,a-b) and (a-b,a+b) (iv) (0,0) and (2,2)

Find the equations of the circles the end points of whose diameter are as follows : (i) (0,6) and (6,0) (ii) (-1,3) and (2,4) (iii) (A+b,a-b) and (a-b,a+b) (iv) (0,0) and (2,2)

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

If a and b are real numbers between o and 1 such that the points (a,0), (1,b) and (0,0) form an equilateral triangle then a=_______ and b=_________.