Answer:
y = 0, y = [tex]\frac{1}{3}[/tex] , y = 7
Step-by-step explanation:
Factor out [tex]y^{\frac{3}{5} }[/tex] from each term
[tex]y^{\frac{3}{5} }[/tex] ( 3[tex]y^{\frac{10}{5} }[/tex] - 22[tex]y^{\frac{5}{5} }[/tex] + 7) = 0 , that is
[tex]y^{\frac{3}{5} }[/tex] (3y² - 22y + 7) = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term
product = 3 × 7 = 21 and sum = - 22
The factors are - 21 and - 1
Use these factors to split the y- term
3y² - 21y - y + 7 ( factor the first/second and third/fourth terms )
3y(y - 7) - 1 (y - 7) ← factor out (y - 7) from each term
(y - 7)(3y - 1)
Then
[tex]y^{\frac{3}{5} }[/tex] (y - 7)(3y - 1) = 0
Equate each factor to zero and solve for y
[tex]y^{\frac{3}{5} }[/tex] = 0 ⇒ y = 0
3y - 1 = 0 ⇒ 3y = 1 ⇒ y = [tex]\frac{1}{3}[/tex]
y - 7 = 0 ⇒ y = 7