Find x^3+8y^3,if xy=2and X+2y=5 Plz solve this
Answers
Answer:
First, use the simultaneous equation method to find x and y by letting the first equation be 3x - 2y = 5 and the second equation be xy = 6.
3x - 2y = 5 (1st equation)
xy = 6 (2nd equation)
In the 2nd equation, move y over to 6 by dividing.
x = \frac{6}{y}
y
6
Then, substitute x into the 1st equation.
3(\frac{6}{y}
y
6
) - 2y = 5
Move 2y over to 5.
3(\frac{6}{y}
y
6
) = 5 + 2y
Multiply 3 with the numerator of the fraction, 6.
\frac{18}{y}
y
18
= 5 + 2y
Move the y on the left side of the equation to the right and multiply.
18 = y(5 + 2y)
18 = 5y + 2y²
Leave the equation in general form by letting the values equal to 0.
2y² + 5y - 18 = 0
Factorise the equation.
(y - 2)(2y + 9) = 0
Solve for the values of y.
y - 2 = 0
y = 2
2y + 9 = 0
2y = -9
y = -9/2
Substitute the values of y into the 2nd equation and solve for x.
x(2) = 6
2x = 6
x = 3
x(-9/2) = 6
x = 6 ÷ -9/2
x = 6 × -2/9
x = -4/3
Now, we will find the values of 27x³ - 8y³.
First, substitute the known values of x and y into the equation.
27(3)³ - 8(2)³
27(-4/3)³ - 8(-9/2)³
Find each of the values to the power of 3.
27(-27) - 8(-8)
27(-64/27) - 8(-729/8)
Multiply 27 and 8 with the numbers in the brackets beside them.
-729 + 64
-64 + 729
Add the numbers.
-665
665
Therefore, the values are -665 and 665.