# Solve the equation ( x^3 + x^2 + 3x - 10 )^1/3 = x.

Asked on by zarvamea

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

(x^3 + x^2 + 3x -10)^1/3 = x

To the 3rd power:

x^3 + x^2 + 3x - 10 = x^3

==> Reduce similar:

==> x^2 + 3x - 10 = 0

==> (x+5)(x-2) = 0

==> x1= -5

==> x2= 2

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll expand to the cube expressions from both sides:

[( x^3 + x^2 + 3x - 10 )^1/3]^3 = x^3

x^3 + x^2 + 3x - 10 = x^3

We'll eliminate like terms:

x^2 + 3x - 10 = 0

We'll apply quadratic formula:

x1 = [-3+sqrt(9+40)]/2

x1 = (-3+7)/2

x1 = 2

x2 = (-3-7)/2

x2 = -5

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve (x^3+x^2+3x-10)^(1/3) = x

Solution:

We cube bothsides:

x^3+x^2+3x-10= x^3. Subtract x^3 from both sides.

x^2+3x-10 = 0

x^2+5x-2x-10 = 0

x(x+5) =2(x+5) = 0

(x+5)(x-2) = 0

x+3=0 or x-2 = 0

x=-3 , or x= 2.

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