SOLUTION: a) √3x-4x^1/2+1=0 b) 5√t=t+4

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Question 1097398: a) √3x-4x^1/2+1=0
b) 5√t=t+4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) +sqrt%283%29x-4sqrt%28x%29%2B1=0+
Use a substitution,
u=sqrt%28x%29
u%5E2=x
So,
sqrt%283%29u%5E2-4u%2B1=0
Using the quadratic formula,

u+=+%284+%2B-+sqrt%28+16-4%2Asqrt%283%29+%29%29%2F%282%2Asqrt%283%29%29+
u+=+%284+%2B-+2sqrt%28+4-sqrt%283%29+%29%29%2F%282%2Asqrt%283%29%29+
u+=+%282%2B-+sqrt%28+4-sqrt%283%29+%29%29%2F%28sqrt%283%29%29+
or approximately,
u=0.2852 and u=2.0242
So then,
x=u%5E2 so,
x=0.0813 and x=4.097
.
.
.
5sqrt%28t%29=t%2B4
25t=%28t%2B4%29%5E2
25t=t%5E2%2B8t%2B16
t%5E2-17t%2B16=0
%28t-16%29%28t-1%29=0
So,
t-16=0
t=16
and
t-1=0
t=1
Verifying,
5%28sqrt%2816%29%29=16%2B4
5%2A4=20
20=20
True, good solution.
and
5%28sqrt%281%29%29=1%2B4
5=5
True, good solution.