Question

If b is the mean Proportional between a and c prove that a,c,a^2+b^2 and b^2+c^2 are Proportional

Answer 1

Answer:

Proved below.

Step-by-step explanation:

Given,

     b is the mean proportional between a and c.

It means : a / b = b / c

⇒ a / b = b / c

⇒ ac = b^2           ...( 1 )

Therefore,

⇒ a / c = a / c

   Dividing and multiplying RHS by ( a + c ) :

⇒ a / c = a( a + c ) / c( a + c )

⇒ a / c = ( a^2 + ac ) / ( ca + c^2 )

⇒ a / c = ( a^2 + b^2 ) / ( b^2 + c^2 )      { using ( 1 ) }

This means a, c , a^2 + b^2 and b^2 + c^2 are in proportion.