Dee D.

asked • 04/11/13

solve for x

6sqrtxy-32y^4 +56y^2 =3y(6y^3+5y)  solve for x

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Inactive Tutor answered • 04/14/13

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You would like to solve this equation for x.
6√(xy) - 32y4 + 56y2 = 3y(6y3 + 5y)

First distribute the 3y.
6√(xy) - 32y4 + 56y2 = 18y4 + 15y2

Next add 32y4 and -56y2 to both sides, and combine like terms. (18+32=50, and 15-56=-41).
6√(xy) = 50y4 - 41y2

Divide by 6 on both sides (and reduce).
√(xy) = (25/3)y4 - (41/6)y2

Square both sides to get rid of the squareroot on the left.
xy = ((25/3)y4 - (41/6)y2)2

FOIL (distribute) the right side (and reduce).
xy = (625/9)y8 - (1025/9)y6 + (1681/36)y4

Divide by y on both sides.
x= (625/9)y7 - (1025/9)y5 + (1681/36)y3

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Inactive Tutor answered • 04/13/13

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6sqrt(xy) - 32y^4 + 56y^2 = 3y(6y^3 + 5y)

6sqrt(xy) - 32y^4 + 56y^2 = 18y^4 + 15y^2

6sqrt(xy) = 18y^4 + 15y^2 + 32y^4 - 56y^2 = 50y^4 - 41y^2

sqrt(xy) = (50/6)y^4 - (41/6)y^2 = (25/3)y^4 - (41/6)y^2 = y^2((25/3)y^2 -  (41/6))

xy = (y^2((25/3)y^2 - (41/6)))^2 = y^4((625/9)y^4 - 2(25/3)y^2(41/6) + (1681/36))

xy = y^4((625/9)y^4 - (1025/9)y^2 + (1681/36))

x = y^3((625/9)y^4 - (1025/9)y^2 + (1681/36))

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