Question

If x, y, z are in A.P, then the statement $\left(x-y\right)\left(y-z\right)=\frac{{\left(z+x\right)}^2}{4}$ is

• A. True
• B. False

Answer 1

The correct option is B False

If $x,y,z$ are in A.P. then we have, $y=\frac{z+x}{2}$.

Now,

$(x-y)(y-z)$

$=(x-\frac{x+z}{2})(\frac{z+x}{2}-z)$

$=\frac{x-z}{2}.\frac{x-z}{2}$

$=\frac{(x-z{)}^2}{4}$.