Question

if (a + b) is directly proportional to √ab then show that (√a + √b) is directly proportional to (√a - √b)

help me guys in this ​

Answer 1

(√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 ...

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Answer 2

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