List of top Mathematics Questions on relationship between a.m. and g.m. asked in KEAM

The sum and difference of the arithmetic mean and the geometric mean of two positive integers are respectively, \(18\) and \(8\). Then the values of the two numbers are

The positive numbers \(\alpha\) and \(\beta\) have geometric mean 6. If \(\alpha\) and \(\beta\) are roots of the equation \(2x^{2} - 25x + \lambda = 0\) then the value of \(\lambda\) is equal to

If A.M. and G.M. of the roots of a quadratic equation are 8 and 5 respectively, then the quadratic equation is

The arithmetic mean (A.M.) of two numbers \( x \) and \( y \) is \( 3 \) and their geometric mean (G.M.) is \( 1 \). Then \( x^2+y^2 \) is equal to:

Two numbers \( x \) and \( y \) have arithmetic mean 9 and geometric mean 4. Then \( x \) and \( y \) are the roots of:

If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is:

If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is:

If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is: