Question

If A.M of the roots of $x^2-2ax+b^2=0$ is equal to the of the roots of the equation $x^2-2bx+a^2=0$. They are in :

• A. A.M
• B. G.M
• C. H.M
• D. None

Answer 1

The correct option is B G.M

$x^2-2ax+b^2=0x=\frac{+2a\pm \sqrt{4a^2-4b^2}}{2}x=\frac{2a\pm 2\sqrt{a^2-b^2}}{2}x=a\pm \sqrt{a^2-b^2}A.M=\frac{a+\sqrt{a^2-b^2}+a-\sqrt{a^2-b^2}}{2}=\frac{2a}{2}=a$
$x^2-2bx+a^2=0x=\frac{+2b\pm \sqrt{4b^2-4a^2}}{2}x=\frac{2b\pm 2\sqrt{b^2-a^2}}{2}x=b\pm \sqrt{b^2-a^2}A.M=b.G.M=b.G.M=\sqrt{(b+\sqrt{b^2-a^2})(b-\sqrt{b^2-a^2})}=\sqrt{b^2-(b^2-a^2)}=\sqrt{b^2-b^2+a^2}=\sqrt{a^2}=a$