Question 761562
I think you are asking for the value of the expression

{{{(z^2 - x^2 + y^2)/(2*y^2)}}}

Given that x/3=y/5=z/7

First, we express x and z in terms of y

{{{x/3 = y/5}}}      Therefore {{{x = 3*y/5}}}

{{{z/7 = y/5}}}      Therefore {{{z = 7*y/5}}}

Now in the given expression, substitute for x and z in terms of y

{{{(z^2 - x^2 + y^2)/(2*y^2)}}}

=

{{{((7*y/5)^2 - (3*y/5)^2 + y^2)/(2*y^2)}}}

=

{{{(49*y^2/25 - 9*y^2/25 + y^2)/(2*y^2)}}}

=

{{{65*y^2/(25*2*y^2)}}}

=

{{{13/10}}}


:)