if (a + b) is directly proportional to √ab then show that (√a + √b) is directly proportional to (√a - √b)
help me guys in this
Answers
(√a + √b) is directly proportional to (√a - √b)
Step-by-step explanation:
(a + b) is directly proportional to √ab
=> a + b = k √ab
to show (√a + √b) is directly proportional to (√a - √b)
let say
(√a + √b) = c and (√a - √b) = d
(√a + √b) = c
squaring both sides
c^2 = a + b + 2√ab
c^2 = k √ab + 2√ab
c^2 = (k +2)√ab
(√a - √b) = d
squaring both sides
d^2 = a + b +- 2√ab
d^2 = k √ab - 2√ab
d^2 = (k - 2)√ab
c^2/d^2 = (k +2)√ab / (k - 2)√ab
c^2/d^2 = (k +2) / (k - 2)
taking square root both sides
c/d = √((k + 2) / (k - 2))
c = d √((k + 2) / (k - 2))
(√a + √b) = (√a - √b) √((k + 2) / (k - 2))
√((k + 2) / (k - 2)) is a constant hence
(√a + √b) is directly proportional to (√a - √b)
QEF
hence proved
learn more :
The variable X is inversely proportional to Y if x increases by P ...
https://brainly.in/question/8648255
hey sova someone deleted Niki's I'd I don't know who maybe Niki herself please unblock me I want to talk u and also want to find Niki I have many questions and things in my mind please unblock me else I will really do something to myself (+_+) ........ please unblock me