What is/are the solution(s) to this equation?

Question

r + 9r^(1/2) + 8= 0

r^(1/2) means the square root of r

Whenever I try to solve the equation i get 1 and 64 as my solutions. When i graph the equation, though, there are no solutions! Please help me

Answer 1

r + 9r^(1/2) + 8 = 0
9r^(1/2) = -(r + 8)
r^(1/2) = -(1/9)(r + 8)

But, you know r>0,
so -(1/9)(r + 8) is always negative

Square both sides,
r = (1/81)(r + 8)^2
81r = r^2 + 64 + 16r
r^2 - 65r + 64 = 0
(r -64)(r -1) = 0
r = 64 or r =1

When you plot the graph,
remember r^(1/2) must be negative not positive.

for r = 64,
64 + 9(64)^(1/2) + 8
= 64 + 9(-8) + 8 (sqrt return -ve)
= 0

for r=1
1 + 9(1)^(1/2) + 8
= 1 + 9(-1) + 8 (sqrt return -ve)
=0

Answer 2

r + 9r^(1/2) + 8= 0

=> r + r^(1/2) + 8r^(1/2) = 8 =0
=> r^(1/2) {r^(1/2) + 1} + 8 {r^(1/2) + 1} = 0
=> {r^(1/2) + 8} {r^(1/2) + 1} = 0
=> r^(1/2) = -8 , -1
=> r = 64 , 1

Substituting, u can get

1 + 9 * (-1) + 8 = 0 as a correct substitution.
or
64 + 9 * (-8) + 8 = 0 also as a correct subsitution.

Answer 3

r+8√r+√r+8=0
√(r)(√(r)+4)+1(√(r)+8)=0
√(r)=-1 √(r)=-8
Actually the ans is no solution as
the sign with√r is positive
a positive sqrt cannot have a negative ans.
eg:
√4cannot be = -2
-√4=-2
If
4=x^2
x=±√4

A question for Amru:
if he were only given 1 and 64
and asked to find the ans. for this equation wud he have substituted -ve roots or +ve roots

Answer 4

factor first.

(r^1/2+1)(r^1/2+8)=0

then solve for 0

r^1/2=-1 r^1/2=-8

Answer 5

If you graph it and you have no solutions,try plugging both of them into the equation and then you'll be able to see if 1 and 64 are solutions.
www.purplemath.com is a good math site.
or you can google it to find help.

Answer 6

let r^1/2=t
t^2+9t+8=0
(t+1)(t+8)=0
t=-1 or -8
r^1/2=-8 or -1
r=64 or 1