Question

$(23-x)$ is mean proportional of $(28-x)$ and $(19-x)$ find the value of x.

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is A 3

Mean proportional of two numbers, $a$ and $b$ is $\sqrt{ab}$
Given, mean proportional of $(28-x)$ and $(19-x)$ is $(23-x)$

$\sqrt{(28-x)\times (19-x)}=(23-x)$

Squaring both sides,

$(28-x)\times (19-x)={(23-x)}^2$
$532-28x-19x+x^2=529+x^2-46x$
$532-47x=529-46x$
$532-529=-46x+47x$
$x=3$