If a, and are in G.P., then find the values(s) of a. contexto.140 3 years ago From the question, Then, Therefore,
![\[\begin{array}{*{35}{l}} {{({{a}^{2}}~+\text{ }2)}^{2}}~=\text{ }a({{a}^{3}}~+\text{ }10) \\ {{a}^{4}}~+\text{ }4\text{ }=\text{ }{{a}^{4}}~+\text{ }10a \\ 4{{a}^{2}}~\text{ }10a\text{ }+\text{ }4\text{ }=\text{ }0 \\ 2{{a}^{2}}~\text{ }5a\text{ }+\text{ }2\text{ }=\text{ }0 \\ 2{{a}^{2}}~\text{ }a\text{ }\text{ }4a\text{ }+\text{ }2\text{ }=\text{ }0 \\ a\left( 2a\text{ }\text{ }1 \right)\text{ }\text{ }2\left( 2a\text{ }\text{ }1 \right)\text{ }=\text{ }0 \\ \left( 2a\text{ }\text{ }1 \right)\text{ }\left( a\text{ }\text{ }2 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b3fd74d1f0977a19f0e9f8be2c930804_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} 2a\text{ }\text{ }1\text{ }=\text{ }0 \\ a\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2} \\ a\text{ }\text{ }2\text{ }=\text{ }0 \\ a\text{ }=\text{ }2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-07e06af5761ee110fdb22930a4ad8bce_l3.png "Rendered by QuickLaTeX.com")
![\[a\text{ }=\text{ }2\text{ }or\text{ }a=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ede0bdb6d4ff95e11cb0b5ce3d526591_l3.png "Rendered by QuickLaTeX.com")
![\[{{\mathbf{a}}^{\mathbf{2}}}+\text{ }\mathbf{2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9b8f3b0b08f5fe838e2457e9d2fe7de6_l3.png "Rendered by QuickLaTeX.com")
![\[{{\mathbf{a}}^{\mathbf{3}}}~+\text{ }\mathbf{10}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b4c50fc8af620213a16c2c059ad4b8af_l3.png "Rendered by QuickLaTeX.com")
