Question

The number of ordered pairs of real numbers (a b) for which 2sqrt(x+3y)+(2)/(sqrt(x+3y))=5 and x=ay+b​

Answer 1

Answer:

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Answer 2

Given : 2√(x + 3y)   + 2/√(x + 3y)  =  5

To find : The number of ordered pairs of real numbers (a b)  

Solution:

2√(x + 3y)   + 2/√(x + 3y)  =  5

Let say √(x + 3y)  = z

=> 2z  + 2/z  = 5

=> 2z² + 2  = 5z

=>  2z² - 5z + 2 = 0

=>2z² - 4z - z + 2 = 0

=> 2z( z - 2) - 1(z _ 2) = 0

=> (2z - 1)(z - 2) = 0

=> z = 1/2  , z  = 2

√(x + 3y)  = 2   or  1/2

=> x + 3y  = 4   or  1/4

=> x  = -3y  + 4     or x    = -3y  + 1/4

Comparing with x  = ay + b

a = - 3  

b = 4  , 1/4

Number of ordered pairs = 2

(-3 , 4)  , (-3  , 1/4)

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