Question

plzzz ans....Thnk u.....Plzz ans FOURTH PART OF IT

Answer 1

since , a , b, c are in continued proportion

=> a : b :: b : c
=> a/b = b/c

=> b² = ac

Now ,

LHS = a²b²c² (a-⁴ + b-⁴ + c-⁴)

=> a² × ac × c² ( 1/a⁴ + 1/(ac)² + 1/c⁴)

=> a² × ac × c² [ (ac)²(c⁴) + (a⁴)(c⁴) + (ac)²(a⁴) ] / a⁴ × c⁴ × (ac)²

=> ( a² × ac × c² ) [ (ac)² [c⁴ + (ac)² + a⁴] / a⁴ × c⁴ × a² × c²

=> a² and c² got cancelled out

=> ac × (ac)² × [ c⁴ + (ac)² + a⁴ ] / a⁴ × c⁴

=> a × a² × c × c² [ c⁴ + (b²)² + a ] / a⁴ × c⁴

a³c³ got cancelled by a⁴ × c⁴ leaving ac in the denominator

=> ( c⁴ + b⁴ + a⁴ ) / ac

=> 1/ ac × ( c⁴+ b⁴ + a⁴ )

=> 1/ b² × ( a⁴ + b⁴ + c⁴ )

=> b-² ( a⁴ + b⁴ + c⁴ )


SINCE , LHS = RHS.

hence , Proved



hope this helps