Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.
Answers
Answer:
9x²+4y²=72
Step-by-step explanation:
3x+2y=12
Squaring on both the sides
(3x+2y)²=(12)²
9x²+4y²+12xy=144
9x²+4y²+12(6)=144
9x²+4y²+72=144
9x²+4y²=144-72
9x²+4y²=72
Answer:
Step-by-step explanation:
To compute the value of 9x^2 + 4y^2, we need to find the values of x and y that satisfy the given equations.
Given:
xy = 6 ...(1)
3x + 2y = 12 ...(2)
We can solve this system of equations using substitution or elimination method.
Let's solve it using the substitution method:
From equation (1), we have xy = 6. We can solve this equation for y:
y = 6/x
Substituting this value of y into equation (2):
3x + 2(6/x) = 12
3x + 12/x = 12
Multiplying through by x to clear the fraction:
3x^2 + 12 = 12x
Rearranging the equation:
3x^2 - 12x + 12 = 0
Dividing through by 3:
x^2 - 4x + 4 = 0
This quadratic equation can be factored as:
(x - 2)^2 = 0
From this, we find that x = 2.
Substituting x = 2 back into equation (1):
2y = 6
y = 3
Now we have x = 2 and y = 3.
Finally, we can compute the value of 9x^2 + 4y^2:
9(2^2) + 4(3^2) = 9(4) + 4(9) = 36 + 36 = 72.
Therefore, the value of 9x^2 + 4y^2 is 72.