Question

if q is the mean proportional between p and r ,prove that : (p²-q²+r²)/(p-² –q-²+r-²) =q⁴.​

Answer 1

Step-by-step explanation:

given q^2 =pr

prove :

(p^2-q^2+r^2)/1/p^2- 1/q^2 +1/ r^2

Answer 2

Answer with 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

#Learns more:

https://brainly.in/question/14572083