To find the values of x and y, we can use the system of equations given:
1) x^2 + y^2 = 12) x*y = 3
First, we can rearrange equation 2) to solve for y in terms of x:
y = 3 / x
Next, we can substitute this into equation 1):
x^2 + (3/x)^2 = 1x^2 + 9/x^2 = 19
Multiplying through by x^2:
x^4 + 9 = 19x^x^4 - 19x^2 + 9 = 0
Let z = x^2:
z^2 - 19z + 9 = 0
Using the quadratic formula to solve for z:
z = [19 ± √(19^2 - 419)] / z = [19 ± √(361 - 36)] / z = [19 ± √325] / 2
z1 = (19 + √325) / z2 = (19 - √325) / 2
Since z = x^2, we take the square root of z to find x:
x1 = √[(19 + √325) / 2x2 = √[(19 - √325) / 2]
From the equation y = 3 / x, we can find the corresponding values of y for x1 and x2:
y1 = 3 / xy2 = 3 / x2
Calculating these values will give us the solutions for x and y.
To find the values of x and y, we can use the system of equations given:
1) x^2 + y^2 = 1
2) x*y = 3
First, we can rearrange equation 2) to solve for y in terms of x:
y = 3 / x
Next, we can substitute this into equation 1):
x^2 + (3/x)^2 = 1
x^2 + 9/x^2 = 19
Multiplying through by x^2:
x^4 + 9 = 19x^
x^4 - 19x^2 + 9 = 0
Let z = x^2:
z^2 - 19z + 9 = 0
Using the quadratic formula to solve for z:
z = [19 ± √(19^2 - 419)] /
z = [19 ± √(361 - 36)] /
z = [19 ± √325] / 2
z1 = (19 + √325) /
z2 = (19 - √325) / 2
Since z = x^2, we take the square root of z to find x:
x1 = √[(19 + √325) / 2
x2 = √[(19 - √325) / 2]
From the equation y = 3 / x, we can find the corresponding values of y for x1 and x2:
y1 = 3 / x
y2 = 3 / x2
Calculating these values will give us the solutions for x and y.