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√x/y+√y/x-5/2=0 and x+y-5=0 we get root as
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√x/y+√y/x-5/2=0 and x+y-5=0 we get root as Related: Chapter - 2 : Equ...
Solution:
Given equations are
√x/y √y/x-5/2=0 and x y-5=0
Let us solve each equation separately.
Solving √x/y √y/x-5/2=0
We can rewrite the equation as
√x/y × √y/x-5/2 = 0
As we know, the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, either √x/y = 0 or √y/x-5/2 = 0.
Solving √x/y = 0 gives x = 0 or y = 0.
Solving √y/x-5/2 = 0 gives y = 0 or x-5/2 = 0, i.e., x = 5/2.
Therefore, the solutions to the equation are (x, y) = (0, 0), (5/2, 0).
Solving x y-5=0
We can rewrite the equation as y = 5/x.
Substituting this in the first equation, we get
√x/(5/x) × √(5/x)/x-5/2 = 0
Simplifying, we get
√x^3/(5(x-5)) = 0
Therefore, the only solution to the equation is x = 0.
Final Answer:
The solutions to the given system of equations are (x, y) = (0, 0), (5/2, 0).
Given equations are
√x/y √y/x-5/2=0 and x y-5=0
Let us solve each equation separately.
Solving √x/y √y/x-5/2=0
We can rewrite the equation as
√x/y × √y/x-5/2 = 0
As we know, the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, either √x/y = 0 or √y/x-5/2 = 0.
Solving √x/y = 0 gives x = 0 or y = 0.
Solving √y/x-5/2 = 0 gives y = 0 or x-5/2 = 0, i.e., x = 5/2.
Therefore, the solutions to the equation are (x, y) = (0, 0), (5/2, 0).
Solving x y-5=0
We can rewrite the equation as y = 5/x.
Substituting this in the first equation, we get
√x/(5/x) × √(5/x)/x-5/2 = 0
Simplifying, we get
√x^3/(5(x-5)) = 0
Therefore, the only solution to the equation is x = 0.
Final Answer:
The solutions to the given system of equations are (x, y) = (0, 0), (5/2, 0).
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