If x^2y^2+x^3y^4=(3xy)^2,then xy^2=
a. 1.5
b.4
c.8
d.16
e.64
x ^ 2 * y ^ 2 + x ^ 3 * y ^ 4 = ( 3 x y ) ^ 2
x ^ 2 * y ^ 2 + x ^ 2 * y ^ 2 ( x * y ^ 2 ) = 9 x ^ 2 * y ^ 2
x ^ 2 * y ^ 2 * ( 1 + x * y ^ 2 ) = 9 * x ^ 2 * y ^ 2 Divide both sides by x ^ 2 * y ^ 2
1 + x * y ^ 2 = 9 Subtract 1 to both sides
1 + x * y ^ 2 - 1 = 9 - 1
x * y ^ 2 = 8
x y ^ 2 = 8
Answer c
To find the value of xy^2, we need to solve the given equation.
Let's start by expanding the expression on the left-hand side of the equation:
x^2y^2 + x^3y^4
We can factor out a common term:
xy^2(x^2 + xy^2)
Now, we can set this equal to the right-hand side:
xy^2(x^2 + xy^2) = (3xy)^2
Since (3xy)^2 is equal to (3^2)(x^2)(y^2), we can simplify the equation further:
xy^2(x^2 + xy^2) = 9x^2y^2
Canceling out the common term, xy^2:
x^2 + xy^2 = 9x^2
Rearranging the equation:
xy^2 = 9x^2 - x^2
Combining like terms:
xy^2 = 8x^2
Now, we need to solve for xy^2. However, we don't have enough information to determine the exact value of x or y. We can say that xy^2 equals 8x^2, but we cannot simplify it further without additional information.
Therefore, the answer cannot be determined based on the given equation. None of the options provided (a. 1.5, b. 4, c. 8, d. 16, e. 64) are correct.