Question

if p,q,r,s are in a proportional then mean proportion between p^2+r^2 & q^2+s^2 is
A)pr/qs
B)pq+rs
C)p/q+s/r
D)p^2/q^2+r^2/s^2​

Answer 1

Answer: The correct Answer to the question is option (B) pq + rs

Step-by-step explanation:

When the equation $\frac{a}{x}$ = $\frac{x}{b}$ is satisfied by a number(x) which comes between the two other numbers (a & b) , the number is said to be mean proportional to the two numbers in Algebra.

For example, 4 satisfies this condition for 1 and 16

$\frac{1}{4}$ = $\frac{4}{16}$  , 4 is said to be the mean proportional between 1 & 16.

Given in the question,

p,q,r,s are in a proportion.

Let the mean proportion be 'X' .

Then, $\frac{(p^2 + r^2)}{X}$ = $\frac{X}{q^2 + s^2}$

X² = ($p^2 + r^2$) ($q^2 + s^2$)  

X² = $p^2q^2$ + $p^2s^2$ + $r^2q^2$ + $r^2s^2$

X² =  $p^2q^2$ + ps.qr + ps.qr + $r^2s^2$ [ since , ps= qr as per proportionality of p,q,r and s ]

X² =  $p^2q^2$  + 2 (pqrs) + $r^2s^2$  

X² = ( pq + rs )²  

X = ( pq + rs )

Mean proportion = ( pq + rs )