Question

Let $a,b,c$ are in AP, then $(a-c{)}^2$ is equal to

• A. $4(b^2-ac)$
• B. $4(b^2+ac)$
• C. $4b^2-ac$
• D. $b^2-4ac$

Answer 1

Answer: (A)

$4(b^2-ac)$

Let $a,b,c$ are in A.P.

as Harmonic mean $b=\left(\frac{a+c}{2}\right)$

Then $2b=a+c$......(1).

Now,

$(a-c{)}^2$$=a^2+c^2-2ac$

$=a^2+c^2-2ac+2ac-2ac$

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

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

$=4b^2-4ac$.....[Using (1)]

$=4(b^2-ac)$

$So$, the answer is option $A$