Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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]
kate200468
[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]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.