Question

Use U-substitution to find the real and imaginary solutions to the following equation:
x-5x^1/2+4=0

Answer 1

try letting u=x^1/2
what is u^2=?

Answer 2

u^2=(x^1/2)^2=? try that

Answer 3

i got down to (x^1/2-4) (x^1/2-1)=0

Answer 4

then i am stuck

Answer 5

no, try substitution of u instead of x

Answer 6

yes i did and then i substituted x^1/2 back in for u

Answer 7

ah ok....
u=x^1/2
u^2=(x^1/2)^2=? x correct? then from
x-5x^1/2+4=0 sub
u^2-5u+4=0 now use quadratic formula to solve for u, then x

Answer 8

yes then i got (u-4) (u-1)

Answer 9

and then substituted x^1/2 back in for u

Answer 10

ok very good, now solve for x
since u=x^1/2

Answer 11

so what do u do when u get to (x^1/2-4) (x^1/2-1)=0

Answer 12

subtract one to the other side?

Answer 13

(u-4) (u-1)=0
u=4,1
u=x^1/2
4=x^1/2 squaring both sides
4^2=(x^1/2)^2
16=x and
1=x^1/2
1=x
therefore x=1 and x=16 ..ans

Answer 14

let me know if u hve question

Answer 15

my teacher instructed me to get to here (x^1/2-4)=(x^1/2-1) and then square both sides.

Answer 16

how would i do this