Question

If $x+5$ is the mean proportion between $x+2$ and $x+9$ find the value of $x$

Answer 1

According to the given condition-

$x+5=\sqrt{(x+2)(x+9)}$

${(x+5)}^2=(x+2)(x+9)$

$x^2+25+10x=x^2+19+11x$

$25+10x=11x+19$

$x=6.$