The number of ordered pairs of real numbers (a, b) for
which 2x + 3y 5 and x = ay + b.
x + 3y
2.
Answers
Given : 2√(x + 3y) + 2/√(x + 3y) = 5
To find : The number of ordered pairs of real numbers (a b)
Solution:
https://brainly.in/question/18701732 - ( complete Question)
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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