Practicing Success
Practicing Success
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If the arithmetic mean and the geometric mean of two numbers a and b are denoted by A and G respectively then form a quadratic equation whose roots are a and b. |
$x^2-Ax+G=0$ $x^2-2Ax+G=0$ $x^2-2A^2G+A=0$ $x^2-2Ax+G^2=0$ |
$x^2-2Ax+G^2=0$ |
a, b, be roots of equation, so equation is x2−(a+b)x+αβ=0 Here, (a+b)/2=A a+b=2A And √a = G √ab = G av = G2 So, Required equation is, x2−2Ax+G2= 0 |
