Question

Find all solutions of the equation. Check your solutions in the original equation.

 8 x^3 − 343=0

Answer 1

`8 x^3-343=0\\\\(2x)^3-7^3=0\ \ \ \ \ \ and\ \ \ \ \ \ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(2x-7)(4x^2+14x+49)=0\\\\2x-7=0\ \ \ or\ \ \ 4x^2+14x+49=0\\2x=7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \Delta=14^2-4\cdot4\cdot49=196-784=-588\\ x= (7)/(2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ no\ solution\\.\ \ \ \ \ \ \ \ Ans.\ x= (7)/(2) \\\\check:\\L=8x^3-343=\\=8\cdot( (7)/(2) )^3-343=8\cdot (7^3)/(2^3) -343=8\cdot (343)/(8) -343=343-343=0`

Answer 2

`8x^3-343=0\ \ \ \ \ |add\ 343\ to\ both\ sides\\\\8x^3=343\ \ \ \ \ \ |divide\ both\ sides\ by\ 8\\\\x^3=(343)/(8)\\\\x=\sqrt[3]{(343)/(8)}\\\\x=\frac{\sqrt[3]{343}}{\sqrt[3]8}\\\\x=(7)/(2)`


`solution:x=(7)/(2)\\\\check:\\\\8\cdot\left((7)/(2)\right)^3-343=0\\\\8\cdot(343)/(8)-343=0\\\\343-343=0\\\\0=0`