Question

If q is the mean proportion between p and r prove that p^2-q^2+r^2/p^-2-q^-2+r^2=q^4

Answer 1

Step-by-step explanation:

q is the mean proportional between p and r

We know that

Mean proportional between two terms of a ratio a: b in a proportional is equal to square root of product of these two terms.

Therefore, q^2=pr

LHS

\frac{p^2-q^2+r^2}{\frac{1}{p^2}-\frac{1}{q^2}+\frac{1}{r^2}}

Substitute the values

\frac{p^2-pr+r^2}{\frac{r^2-pr+p^2}{p^2r^2}}

\frac{p^2-pr+r^2}{p^2-pr+r^2}\times p^2r^2

p^2r^2=(pr)^2

(q^2)^2

q^4

LHS=RHS

Hence, proved