%5E2%2B(y-1%2F10)%5E4-%3D0.jpeg "(x-3 5)^2+(y-1/10)^4 =0")
Solving the Equation (x-3/5)^2 + (y-1/10)^4 = 0
In this article, we will explore the solution to the equation (x-3/5)^2 + (y-1/10)^4 = 0. This equation involves a combination of quadratic and quartic terms, making it a challenging problem to solve.
Expanding the Equation
To begin, let's expand both terms of the equation:
(x-3/5)^2 = x^2 - (6/5)x + 9/25 (y-1/10)^4 = y^4 - (4/10)y^3 + (6/100)y^2 - (4/1000)y + 1/10000
Now, we can rewrite the original equation as:
x^2 - (6/5)x + 9/25 + y^4 - (4/10)y^3 + (6/100)y^2 - (4/1000)y + 1/10000 = 0
Simplifying the Equation
To simplify the equation, we can start by combining like terms:
x^2 - (6/5)x + y^4 - (4/10)y^3 + (6/100)y^2 - (4/1000)y + 1/10000 + 9/25 = 0
Next, we can rearrange the terms to group the x and y terms separately:
(x^2 - (6/5)x + 9/25) + (y^4 - (4/10)y^3 + (6/100)y^2 - (4/1000)y + 1/10000) = 0
Solving for x and y
Now, we can solve for x and y separately.
Solving for x
x^2 - (6/5)x + 9/25 = 0
We can factor the quadratic equation:
(x - 3/5)(x - 3/5) = 0
This implies that x - 3/5 = 0, so x = 3/5.
Solving for y
y^4 - (4/10)y^3 + (6/100)y^2 - (4/1000)y + 1/10000 = 0
This is a quartic equation, which is more challenging to solve. However, we can try to factor the equation:
(y - 1/10)(y - 1/10)(y - 1/10)(y - 1/10) = 0
This implies that y - 1/10 = 0, so y = 1/10.
Conclusion
In conclusion, the solution to the equation (x-3/5)^2 + (y-1/10)^4 = 0 is x = 3/5 and y = 1/10.
