Question

If a,b,c are in AP prove that bc - a^2, ca - b^2, ab - c^2 are in AP

Answer 1

Answer:

Hope this answer helps you

Answer 2

Answer:

$\huge\bold\red{ANSWER}$

Step-by-step explanation:

$\large{\underline{\rm{\red{SOLUTION :}}}}$

$\implies$ if a,b,c are in AP then (b-a)=(c-b)

$\implies$ from the second apply (b-a)=(c-b)

     $\sf{(ca-b^2)-(bc-a^2)}$

     $\sf{(a-b)(a+b+c)}$

     $\sf{-(b-a)(a+b+c)}$

 $\sf{and\:(ab-c^2)-(ca-b^2)}$

       $\sf{(b-c)(a+b+c)}$

      $\sf{-(c-b)(a+b+c)}$

from both equations

      $\sf{(ca-b^2)-(bc-a^2)=(ab-c^2)-(ca-b^2)}$

      $\sf{therefore\: they\: are\: in\: AP}$