Question

if a, b, c is in Ap prove that (a-c) ^2=4(b^2-ac)​

Answer 1

Answer:

$\bf{(a-c)^2=4(b^2-ac)}$

Step-by-step explanation:

$\text{Concept used:}$

$\text{If a, b and c are in A.P, then}\:b=\frac{a+c}{2}$

Given:

$\text{a, b and c are in A.P}$

$\text{Then}\:b=\frac{a+c}{2}$

$\implies\:2b=a+c$

$\text{Now,}$

$(a-c)^2$

$=(a+c)^2-4ac$

$=(2b)^2-4ac$

$=4b^2-4ac$

$=4(b^2-ac)$

$\implies\:\bf{(a-c)^2=4(b^2-ac)}$