392 - example on ratios

 392 - example on ratios

 

Example on Ratios

===============

 

If a/b = c/d = e/f , then show that

 

(a^3 + 2(c^2)e - 2 a(e^2)f )              ace

----------------------------------------- = ------

( b^4 + 2 (d^2) f - 3b(f^3) )              bdf

 

Let us take the following assumptiion

a/b = c/d = e/f = k

where , k is any constant which we assign it to the

ratios as a number equivalent to the ratios of these

Numbers

 

Now ,

a = bk , c = dk , e = fk

 

therefore ,

 

( (a^3)b+2(c^2)e - 3a(e^2)f )

-------------------------------------

( b^4 + 2(d^2)f - 3b(f^3) )

 

=

(b^4)(k^3) + 2(d^2)(k^2)(fk) - 3(bk)(f^2)(k^2)f

-------------------------------------------------------------------

b^4 + 2(d^2)f - 3(b)(f^3)

 

=(k^3)

= k*k*k

= (a/b)*(c/d)*(e/f)

= ace / bdf