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Find all solutions of the equation. Check your solutions in the original equation. 8 x^3 − 343=0

Sagot :

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

[tex]solution:x=\frac{7}{2}\\\\check:\\\\8\cdot\left(\frac{7}{2}\right)^3-343=0\\\\8\cdot\frac{343}{8}-343=0\\\\343-343=0\\\\0=0[/tex]
Kate200468idn
[tex]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= \frac{7}{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ no\ solution\\.\ \ \ \ \ \ \ \ Ans.\ x= \frac{7}{2} \\\\check:\\L=8x^3-343=\\=8\cdot( \frac{7}{2} )^3-343=8\cdot \frac{7^3}{2^3} -343=8\cdot \frac{343}{8} -343=343-343=0[/tex]
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