Question

P +1/q =4 q +1/r =1 r 1/p =7/3 pqr=?

Answer 1

Answer:

pqr=1

Step-by-step explanation:

Given,

p + 1/q = 4 --------(1)

q + 1/r = 1 ---------(2)

r + 1/p = 7/3 -------(3)

from equation (1), p + 1/q = 4

⇒ 1/q = 4 - p

put it in equation (2),

1/(4 - p) + 1/r = 1

⇒1/(4 - p) - 1 = - 1/r

⇒(1 - 4 + p)/(4 - p) = -1/r

⇒ (3 - p)/(4 - p) = 1/r

⇒ r = (4 - p)/(3 - p) , put it in equation (3)

(4 - p)/(3 - p) + 1/p = 7/3

⇒{(4 - p)p + (3 - p)}/p(3 - p) = 7/3

⇒ {4p - p² + 3 - p }/(3p - p²) = 7/3

⇒(-p² + 3p + 3 )/(3p - p²) = 7/3

⇒-3p² + 9p + 9 = 21p - 7p²

⇒4p² - 12p + 9 = 0

⇒ (2p - 3)² = 0 ⇒ p = 3/2

put p = 3/2 in equation (3),

r + 2/3 = 7/3

r = 5/3

Now, r = 5/3 put in equation (2),

q + 3/5 = 1

q = 2/5

Hence, pqr = 3/2 × 5/3 × 2/5 = 1

pqr = 1