Question

a segment AB of 2m length is divided at c into two parts such that AC2=AB*CB. find the length of CB

Answer 1

i think that it may be right answer

Answer 2

Given:

Length of segment AB=2 m

$AC^2=AB\times CB$

To find:

Length of CB

Solution:

By using segment addition property

AB=AC+CB

AC=AB-CB

Substitute the value

$(AB-CB)^2=2CB$

$(2-CB)^2=2CB$

$4-4CB+CB^2=2CB$

Using identity

$(a-b)^2=a^2+b^2-2ab$

$CB^2-4CB-2CB+4=0$

$CB^2-6CB+4=0$

$CB=\frac{6\pm\sqrt{36-16}}{2}$

Using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$CB=\frac{6\pm 2\sqrt{5}}{2}=3\pm\sqrt 5$

$CB=3+\sqrt{5}=5.24 m$

It is not possible because CB cannot be greater than AB

$CB=3-\sqrt{5}= 0.76 m$

Hence, the length of CB=0.76 m