SOLUTION: My question is: Solve this equation algebraically
x^5=3x+2x^3y
and: Find all the solutions algebraically
1) Sqroot(x) − Sqroot(x − 5) = 1
2)3x(x-1)^(1/2)+2
Algebra.Com
Question 478840: My question is: Solve this equation algebraically
x^5=3x+2x^3y
and: Find all the solutions algebraically
1) Sqroot(x) − Sqroot(x − 5) = 1
2)3x(x-1)^(1/2)+2(x-1)^(1/2)=0
If you can please explain how to solve it for future reference. Thank You :)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve this equation algebraically
x^5 = 3x + 2x^3y
x^5 - 2x^3y = 3x
Factor out x^3
x^3(x^2 - 2y) = 3x
divide both sides by x
x^2(x^2 - 2y) = 3
x^2 - 2y =
-2y = - x^2
Divide both sides by -2
y = +
put over a single denominator
y =
y =
Solve for x
= 0
Divide both sides by 2x^2
x^4 - 3 = 0
x^4 = 3
x = 3^(1/4)
x = +/- 1.316
:
:
Find all the solutions algebraically
1) = 1
Rearrange this to
Square both sides
= x - 5
FOIL the left side
x - 2( + 1 = x - 5
-2( = x -x - 5 - 1
-2( = -6
Square both sides again
4x = 36
x =
x = 9
Check this in the original equation
:
:
2)=0
=
Square both sides
9x^2(x-1) = 4(x-1)
divide both sides by (x-1), leaving us with
9x^2 = 4
Find the square root of both sides
3x = 2
x = , sadly, this will work in the original equation, no solution for x
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