2∛(2x + 1) = x3 – 1
solve for x
Answers
Answered by
2
Answer:
We have
3
(2x−1)
+
3
(x−1)
=1............(1)
Cubing both sides of (1) , we obtain
2x−1+x−1+3
3
(2x−1)(x−1)
(
3
(2x−1)
+
3
(x−1)
)=1
⇒3x−2+3.
3
(2x
2
−3x+1)
(1)=1 {from(1)}
⇒3.
3
(2x
2
−3x+1)
=3−3x
⇒
3
(2x
2
−3x+1)
=(1−x)
again cubing both sides, we obtain
2x
2
−3x+1=(1−x)
3
⇒(2x−1)(x−1)=(1−x)
3
⇒(2x−1)(x−1)=−(x−1)
3
⇒(x−1){2x−1+(x−1)
2
}=0
⇒(x−1)(x)
2
=0
∴x
1
=0andx
2
=1
∵x
1
=0 is not satisfied the equation (1) then x
1
=0 is an extraneous root of the equation (1) thus x
2
=1 is the only root of the original equation.
Similar questions