Question

if a , b and c are in continued proportion , shiw that : a^2 +b^2/b(a+c) = b(a+c ) / b^2+ c^2​

Answer 1

Answer:

( a^2 + b^2 ) / b( a + c ) = b( a + c ) / ( b^2 + c^2 )

Step-by-step explanation:

We know, if x , y and z are given in continued proportion, it means :

• x / y = y / z .

Here, a , b and c are given in continued proportion, so

= > a / b = b / c

= > a x c = b x b

= > ac = b^2

Then,

= > a / b = b / c

Multiply and divide both sides by ( a + c ) :

= > { a( a + c ) } / { b( a + c ) } = { b( a + c ) } / { c( a + c ) }

= > { a^2 + ac } / { b( a + c ) } = { b( a + c ) } / { ac + c^2 }

= > ( a^2 + b^2 ) / b( a + c ) = b( a + c ) / ( b^2 + c^2 ) { from above, ac = b^2 }

Hence proved.