(i)
![\[\mathbf{3}{{\left( \mathbf{x}\text{ }\text{ }\mathbf{2} \right)}^{\mathbf{2}}}~=\text{ }\mathbf{147}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0444fd52cd031f17285a34c21b62524b_l3.png "Rendered by QuickLaTeX.com")
Firstly let us expand the given expression,
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6edbc46379d28ca1386ece0d814edcb3_l3.png" height="158" width="360" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & \begin{array}{*{35}{l}} 3({{x}^{2}}~\text{ }4x\text{ }+\text{ }4)\text{ }=\text{ }147 \\ 3{{x}^{2}}~\text{ }12x\text{ }+\text{ }12\text{ }=\text{ }147 \\ 3{{x}^{2}}~\text{ }12x\text{ }+12\text{ }\text{ }147\text{ }=\text{ }0 \\ \end{array} \\ & 3{{x}^{2}}~\text{ }12x\text{ }\text{ }135\text{ }=\text{ }0 \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e43cab876d681fdd977380ec0fa8230e_l3.png "Rendered by QuickLaTeX.com")
Divide by
![\[3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-df8bcc09db12acd0f6bda88b4b8135fb_l3.png "Rendered by QuickLaTeX.com")
, we get
![\[{{x}^{2}}~\text{ }4x\text{ }\text{ }45\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6ac984f3569e7a9732170877a65aebc5_l3.png "Rendered by QuickLaTeX.com")
Let us factorize the expression,
![\[\begin{array}{*{35}{l}} {{x}^{2}}~\text{ }9x\text{ }+\text{ }5x\text{ }\text{ }45\text{ }=\text{ }0 \\ x\left( x\text{ }\text{ }9 \right)\text{ }+\text{ }5\left( x\text{ }\text{ }9 \right)\text{ }=\text{ }0 \\ \left( x\text{ }+\text{ }5 \right)\text{ }\left( x\text{ }\text{ }9 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5c1bcb2378dacc739f2446397f616005_l3.png "Rendered by QuickLaTeX.com")
So now,
![\[\begin{array}{*{35}{l}} \left( x\text{ }+\text{ }5 \right)\text{ }=\text{ }0\text{ }or\text{ }\left( x\text{ }\text{ }9 \right)\text{ }=\text{ }0 \\ x\text{ }=\text{ }-5\text{ }or\text{ }x\text{ }=\text{ }9 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-78ec33877d3d4a2baaec805d39c22863_l3.png "Rendered by QuickLaTeX.com")
∴ Value of x =
![\[-5,\text{ }9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cad21e6df39a786cc384f127505e8f65_l3.png "Rendered by QuickLaTeX.com")
(ii)
![\[\mathbf{1}/\mathbf{7}\left( \mathbf{3x}\text{ }\text{ }\mathbf{5} \right){}^\text{2}\text{ }=\text{ }\mathbf{28}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bd5941c7852d7e37204b72b73442dbfd_l3.png "Rendered by QuickLaTeX.com")
Let us simplify the expression,
![\[\begin{array}{*{35}{l}} {{\left( 3x\text{ }\text{ }5 \right)}^{2}}~=\text{ }28\text{ }\times \text{ }7 \\ {{\left( 3x\text{ }\text{ }5 \right)}^{2}}~=\text{ }196 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-017f2c94bef470c4142e8e2d4b7e9c76_l3.png "Rendered by QuickLaTeX.com")
Now let us expand,
![\[\begin{array}{*{35}{l}} 9{{x}^{2}}~\text{ }30x\text{ }+\text{ }25\text{ }=\text{ }196 \\ 9{{x}^{2}}~\text{ }30x\text{ }+\text{ }25\text{ }\text{ }196\text{ }=\text{ }0 \\ 9{{x}^{2}}~\text{ }30x\text{ }\text{ }171\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7a551c09c3b74e83c3cb51bdd4c61ef6_l3.png "Rendered by QuickLaTeX.com")
Divide by
, we get
![\[3{{x}^{2}}~\text{ }10x\text{ }\text{ }57\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-42c898401b5db480e74d2f473466e894_l3.png "Rendered by QuickLaTeX.com")
Let us factorize the expression,
![\[\begin{array}{*{35}{l}} 3{{x}^{2}}~\text{ }19x\text{ }+\text{ }9x\text{ }\text{ }57\text{ }=\text{ }0 \\ x\left( 3x\text{ }\text{ }19 \right)\text{ }+\text{ }3\left( 3x\text{ }\text{ }19 \right)\text{ }=\text{ }0 \\ \left( x\text{ }+\text{ }3 \right)\text{ }\left( 3x\text{ }\text{ }19 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-296d53ef1a95ac7447a0bae08ca7745a_l3.png "Rendered by QuickLaTeX.com")
So now,
![\[\begin{array}{*{35}{l}} \left( x\text{ }+\text{ }3 \right)\text{ }=\text{ }0\text{ }or\text{ }\left( 3x\text{ }\text{ }19 \right)\text{ }=\text{ }0 \\ x\text{ }=\text{ }-3\text{ }or\text{ }3x\text{ }=\text{ }19 \\ x\text{ }=\text{ }-3\text{ }or\text{ }x\text{ }=\text{ }19/3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-54416f875618ff5c53ee78e2c9b197a1_l3.png "Rendered by QuickLaTeX.com")
∴ Value of x =
![\[-3,\text{ }19/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-63d2734b443cd384fce6c086b134feb8_l3.png "Rendered by QuickLaTeX.com")
