{"id":1977,"date":"2023-06-26T13:34:00","date_gmt":"2023-06-26T17:34:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=1977"},"modified":"2024-10-25T12:03:07","modified_gmt":"2024-10-25T16:03:07","slug":"algebra-challenge-1-%e2%ad%90","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=1977","title":{"rendered":"Algebra Challenge &#8211; 1 \u2b50"},"content":{"rendered":"\n<p>If $x=\\sqrt[3]{9}+\\sqrt[3]{3}+1$, find the value of $(\\dfrac{2}{x}+1\\big{)}^3$. Click <a href=\"javascript:toggle_visibility('alg-chall-1-sol')\">here<\/a> for the solution.<\/p>\n\n\n\n<div id=\"alg-chall-1-sol\" style=\"display:none\">\n<p><strong>Solution<\/strong>: Let $y=\\sqrt[3]{3}$, we have $$x=y^2+y+1=\\dfrac{y^3-1}{y-1}=\\dfrac{(\\sqrt[3]{3})^3-1}{\\sqrt[3]{3}-1}=\\dfrac{2}{\\sqrt[3]{3}-1}$$ Therefore $$(\\dfrac{2}{x}+1)^3=(2\\cdot \\dfrac{\\sqrt[3]{3}-1}{2}+1)^3=(\\sqrt[3]{3})^3=\\boxed{3}$$<\/p>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>If $x=\\sqrt[3]{9}+\\sqrt[3]{3}+1$, find the value of $(\\dfrac{2}{x}+1\\big{)}^3$. Click here for the solution. Solution: Let $y=\\sqrt[3]{3}$, we have $$x=y^2+y+1=\\dfrac{y^3-1}{y-1}=\\dfrac{(\\sqrt[3]{3})^3-1}{\\sqrt[3]{3}-1}=\\dfrac{2}{\\sqrt[3]{3}-1}$$ Therefore $$(\\dfrac{2}{x}+1)^3=(2\\cdot \\dfrac{\\sqrt[3]{3}-1}{2}+1)^3=(\\sqrt[3]{3})^3=\\boxed{3}$$<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[13,14],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/1977"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1977"}],"version-history":[{"count":17,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/1977\/revisions"}],"predecessor-version":[{"id":2136,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/1977\/revisions\/2136"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}