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Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
Answer:
So, the correct option is A. x = 9, y = 14 , Sides are 11 and 20
Step-by-step explanation:
P.S - the exact question is -
As given in the question ,
Side AB = Side AD
⇒y - 3 = x + 2
⇒y - x = 2 + 3 = 5
⇒y - x = 5 .........(1)
Also, given
Side BC = Side CD
⇒2x + 2 = x + 11
⇒2x - x = 11 - 2
⇒x = 9
∴ equation (1) becomes
y - 9 = 5
⇒y = 5 + 9 = 14
⇒y = 14
∴ we get
x = 9, y = 14
Now,
as given ,
Side AB = y - 3
⇒ AB = 14 - 3 = 11
Side BC = 2x + 2
⇒ BC = 2(9) + 2 = 18 + 2 = 20
Side CD = x + 11
⇒ CD = 9 + 11 = 20
Side DA = x + 2
⇒DA = 9 + 2 = 11
∴ we get
The sides are 11 and 20
So,
The correct option is A. x = 9, y = 14 , Sides are 11 and 20
