![\[\mathbf{13}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7fb6d31e24c140ffa47495dad024f968_l3.png "Rendered by QuickLaTeX.com")
![\[~\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{a}\text{ }+\text{ }\mathbf{b}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c579386c91f38559d0502077b0c28298_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{x}/{{\mathbf{a}}^{\mathbf{2}~}}+\text{ }\mathbf{y}/{{\mathbf{b}}^{\mathbf{2}~}}=\text{ }\mathbf{2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f6409fd41a44fdf12abbb99cf27f71d4_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{14}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-24ab512b15a55f61669f820d17013339_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{x}/\mathbf{a}\text{ }=\text{ }\mathbf{y}/\mathbf{b}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-402b04d9fe104eb74724f117540a92ad_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{ax}\text{ }+\text{ }\mathbf{by}\text{ }=\text{ }{{\mathbf{a}}^{\mathbf{2}}}~+\text{ }{{\mathbf{b}}^{\mathbf{2}}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b00275c95aaf17b6fff2bfe7f063074a_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given
![\[x/a\text{ }+\text{ }y/b\text{ }\text{ }\left( a\text{ }+\text{ }b \right)~=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e0d284a89b6e2f2248f9788df5e8c4b6_l3.png "Rendered by QuickLaTeX.com")
![\[x/{{a}^{2~}}+\text{ }y/{{b}^{2~}}\text{ }2~=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8fb8a69f39a5c07a99cb500df44a6474_l3.png "Rendered by QuickLaTeX.com")
Cross multiplication Method
![\[\frac{x}{{{b}_{1}}{{c}_{2}}-{{b}_{2}}{{c}_{1}}}=\frac{-y}{{{a}_{1}}{{c}_{2}}-{{a}_{2}}{{c}_{1}}}=\frac{1}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-007fa7175ae1f5c3950c34825b73ca25_l3.png "Rendered by QuickLaTeX.com")
Comparing the two equations
![\[{{a}_{1}}=\frac{1}{a},\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0200af07ee6824a6ff78430e31a62a20_l3.png "Rendered by QuickLaTeX.com")
![\[{{b}_{1}}=\frac{1}{b},\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56d1bd0abec514d7269b0a3c51ec9544_l3.png "Rendered by QuickLaTeX.com")
![\[{{c}_{1}}=\left( a+b \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cfaf0572b3d6c5fea492b442fb094cce_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{2}}=\frac{1}{{{a}^{2}}},{{b}_{2}}=\frac{1}{{{b}^{2}}},{{c}_{2}}=-2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d8b4119d8123fa4bb0f05f5dcb73ff73_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{x}{\frac{a-b}{{{b}^{2}}}}=\frac{-y}{\frac{-a-b}{{{a}^{2}}}+\frac{1}{a}+\frac{b}{{{a}^{2}}}}=\frac{1}{\frac{-1}{a{{b}^{2}}}-\frac{-1}{a2b}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d84b296d4b18e54350200a5d933ea8ae_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{x}{\frac{a-b}{{{b}^{2}}}}=\frac{1}{\frac{-1}{a{{b}^{2}}}-\frac{-1}{a2b}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f055bafb967ecb52ff7076545b7a9b56_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{-y}{\frac{-a-b}{{{a}^{2}}}+\frac{1}{a}+\frac{b}{{{a}^{2}}}}=\frac{1}{\frac{-1}{a{{b}^{2}}}-\frac{-1}{a2b}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8cb8acdbfc6941cb2eb83a5fa0388713_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given
![\[x/a\text{ }\text{ }y/b~=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-339e59d2b32b298adb3900531956eb1a_l3.png "Rendered by QuickLaTeX.com")
![\[ax\text{ }+\text{ }by\text{ }\text{ }\left( {{a}^{2}}~+\text{ }{{b}^{2}} \right)~=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7bd0ce48413bcc32d4a193f571204f47_l3.png "Rendered by QuickLaTeX.com")
Cross multiplication Method
Comparing the two equations
![\[{{c}_{1}}=0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d8c548b5bba9ca0e65c89b7b9f78a01d_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{1}}=a,{{b}_{1}}=b\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a5e3a56465fb1a31004324769b108154_l3.png "Rendered by QuickLaTeX.com")
![\[{{c}_{1}}=\left( {{a}^{2}}+{{b}^{2}} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-706493c025e91d07f5d37ade8792e634_l3.png "Rendered by QuickLaTeX.com")
=
And,
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