Question

I have to solve each equation using a u substitution and need help understanding how to do this.

The first equation is:
1. x^2/3-2x^1/3-15=0

2. x+4=7 Squareroot x+4

Answer 1

x^2/3-2x^1/3-15=0
(x^(1/3))^2 - 2x^(1/3) - 15 = 0
suppose we let x^(1/3) = y, then we get

y^2 - 2y - 15 = 0
(y-5)(x+3) = 0
y = 5 or y = -3

then x^(1/3)= 5 , cube both sides
x = 125
or
x^(1/3) = -3
x = -27

2.
x+4 = 7√(x+4)
square both sides
x^2 + 8x + 16 = 49(x+4)
x^2 + 8x + 16 = 49x +196
x^2 - 41x - 180=0
(x-45)(x+4) = 0
x = 45 or x = -4

BUT, since we squared, we must verify all answers
if x = 45
LS = 45+4 = 49
RS = 7√49 = 49 , works

if x = -4
LS = 0
RS = 7√0 = 0 , works

so x = 45 or x = -4

Answer 2

Thank you so much this makes the examples provided make much more scense the way you broke them down! Thanks!