(2) If \( (28-x) \) is the mean proportional of \( (23-x) \) and \( (19-x) \) then find the value of \( x \).
(3) Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26 , then find these numbers.
(4) If \( (a+b+c)(a-b+c)=a^{2}+b^{2}+c^{2} \) show that \( a, b, c \) are in continued proportion.
(5) If \( \frac{a}{b}=\frac{b}{c} \) and \( a, b, c>0 \) then show that,
(i) \( (a+b+c)(b-c)=a b-c^{2} \)
(ii) \( \left(a^{2}+b^{2}\right)\left(b^{2}+c^{2}\right)=(a b+b c)^{2} \)
(iii) \( \frac{a^{2}+b^{2}}{a b}=\frac{a+c}{b} \)
Find mean proportional of \( \frac{x+y}{x-y}, \frac{x^{2}-y^{2}}{x^{2} y^{2}} \)
