Question

the number of ordered pairs of real numbers (a,b) for which 3rootx-2y + 3upon rootx-2y =10 and x=ay+b

Answer 1

Answer:

(2 , 9 )  & (2 , 1/9)

Step-by-step explanation:

the number of ordered pairs of real numbers (a,b) for which 3rootx-2y + 3upon rootx-2y =10 and x=ay+b

3√(x - 2y)   +  3/√(x - 2y)   = 10

let say √(x - 2y) = k

3k + 3/k = 10

=> 3k² + 3 = 10k

=> 3k² - 10k + 3 = 0

=> 3k² - 9k - k + 3 = 0

=> 3k(k -3) -1(k-3) = 0

=> (3k -1)(k-3) = 0

=> k = 1/3  or k = 3

case 1

√(x - 2y)  = 3

squaring both sides

x  - 2y = 9

x = 2y + 9

comparing with x = ay + b

a =2 & b = 9

Case 2

√(x - 2y)  = 1/3

squaring both sides

x - 2y = 1/9

=> x = 2y + 1/9

a =2 & b = 1/9

Answer 2

Answer:

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Step-by-step explanation:

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