From the question,
![\[\begin{array}{*{35}{l}} {{x}^{2}}~=\text{ }-2/7\text{ }\times \text{ }-7/2 \\ {{x}^{2}}~=\text{ }1 \\ x\text{ }=\text{ }\pm \text{ }1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a6d6ea677b9a69bfe22afa99250cfa84_l3.png "Rendered by QuickLaTeX.com")
Therefore,
![\[x\text{ }=\text{ }1\text{ }or\text{ }x\text{ }=\text{ }\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-39d17bd6ed26bb9de68cc5d14758ba73_l3.png "Rendered by QuickLaTeX.com")
(ii)
![\[\mathbf{x}\text{ }+\text{ }\mathbf{9},\text{ }\mathbf{x}\text{ }\text{ }\mathbf{6}\text{ }\mathbf{and}\text{ }\mathbf{4}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d75c0a43231654fc538f474f6fb2b21e_l3.png "Rendered by QuickLaTeX.com")
are three consecutive terms of a G.P.
Solution:-
From the question,
![\[\begin{array}{*{35}{l}} {{\left( x\text{ }\text{ }6 \right)}^{2}}~=\text{ }\left( x\text{ }+\text{ }9 \right)\text{ }\times \text{ }4 \\ {{x}^{2}}~\text{ }12x\text{ }+\text{ }36\text{ }=\text{ }4x\text{ }+\text{ }36 \\ {{x}^{2}}~\text{ }12x\text{ }\text{ }4x\text{ }+\text{ }36\text{ }\text{ }36\text{ }=\text{ }0 \\ {{x}^{2}}~\text{ }16x\text{ }=\text{ }0 \\ x\left( x\text{ }\text{ }16 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-585dde75386d62deb8e2ad65f58fe1db_l3.png "Rendered by QuickLaTeX.com")
Either let us take
![\[x\text{ }\text{ }16\text{ }=\text{ }16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1d773aa0b6234dd6c75fab80f8378d65_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}}</strong> <strong> Or\text{ }x\text{ }=\text{ }0 \\</strong> <strong> So,\text{ }x\text{ }=\text{ }0,\text{ }16 \\</strong> <strong>\end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51b66f620e0e82092dfdbba16629cffa_l3.png "Rendered by QuickLaTeX.com")
Find the value of x such that, (i)
![\[-\mathbf{2}/\mathbf{7},\text{ }\mathbf{x},\text{ }-\mathbf{7}/\mathbf{2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ca07fa264d9c2f9c42a33433dadfba95_l3.png "Rendered by QuickLaTeX.com")
From the question,
Therefore,
(ii)
are three consecutive terms of a G.P.
Solution:-
From the question,
Either let us take
