The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`

If three unequel numbers are in HP and their squares are in AP, show that they are in the ratio 1+sqrt(3):-2:1-sqrt(3) " or " 1-sqrt(3):-2:1+sqrt(3) .

If the arithmetic means of two positive number a and b (a gt b ) is twice their geometric mean, then find the ratio a: b

Classify the following numbers as rational or irrational. (2+sqrt2)(2-sqrt2)

rationalising the denominator: (1)/(3sqrt2-2sqrt3)

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G^2=27. Find two numbers.

The A.M and G.M of two numbers are in the ratio 3: 2, then the ratio of the numbers is

rationalising the denominator: (6-4sqrt2)/(6+4sqrt2)

Show that 3sqrt2 is irrational.

Classify the following numbers as rational or irrational. sqrt3+sqrt2

If the geometric mean is (1)/(n) times the harmonic mean between two numbers, then show that the ratio of the two numbers is 1+sqrt(1-n^(2)):1-sqrt(1-n^(2)) .