Question

Solve the cube root equation 2x2−−−√3=3−5x−−−−−−√3
.(1 point)
Responses

x=52
and x=1
x equals Start Fraction 5 over 2 End Fraction and x equals 1

x=−3
and x=12
x equals negative 3 and x equals Start Fraction 1 over 2 End Fraction

x=−52
and x=1
x equals negative Start Fraction 5 over 2 End Fraction and x equals 1

x=1
and x=32

Answer 1

Assuming the cube roots are equal, their radicands are equal:
2x^2 − √3 = 3 − 5x − √3
Cancel √3 and solve:
2x^2 + 5x − 3 = 0
Factor: (2x − 1)(x + 3) = 0
So x = 1/2 or x = −3.

Answer: x = −3 and x = 1/2.