Question

2x³-8=0 How do I solve this problem ?

Answer 1

Answer:

$x=2^{\frac{2}{3}}$

Step-by-step explanation:

1) Add 8 to both sides.

<em />$2x^3=8$

2) Divide both sides by 2.

$x^3=\frac{8}{2}$

3) Simplify $\frac{8}{2}$ to 4.

$x^3=4$

4) Take the cube root of both sides.

$x=\sqrt[3]{4}$

5) Rewrite 4 as 2².

$x=\sqrt[3]{2^2}$

6) Use this rule: ${({x}^{a})}^{b}={x}^{ab}$.

$x=2^{\frac{2}{3}}$

Decimal Form: 1.587401

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Check the answer:

$2x^3-8=0$

1) Let $x=2^\frac{2}{3}$.

$2(2^{\frac{2}{3} })-8=0$

2) Use this rule: $(x^a)^b=x^{ab}$.

$2\times2^{\frac{2\times3}{3} } -8=0$

3) Simplify 2 * 3 to 6.

$2\times2^{\frac{6}{3} } - 8 =0$

4) Simplify 6/3 to 2.

$2\times2^2-8=0$

5) Use Product Rule: $x^ax^b=x^{a+b}$.

$2^3-8=0$

6) Simplify 2^3 to 8.

8 - 8 = 0

7) Simplify 8 - 8 to 0.

0 = 0

Thank you,

Eddie