[tex]\large{\tt{12:43\:nn\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:3/2/22}}[/tex]
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Solve for x: [tex]\rm{8x^{2} - 3 = 2}[/tex]
- [tex]\Large\sf{\underline{\green{x = \dfrac{\sqrt{10}}{4}, -\dfrac{\sqrt{10}}{4}}}}[/tex]
[tex]\\[/tex]
[tex]\huge{\red{\boxed{\gray{\mathbb{SOLUTION}}}}}[/tex]
» We can solve this question by using the method of finding the square root.
» The given equation is:
- [tex]\rm{8x^{2} - 3 =2}[/tex]
» Add 3 to both the sides of the equation:
- [tex]\rm{8x^{2} = 2 + 3}[/tex]
» Now, add 2 & 3 to get 5:
- [tex]\rm{8x^{2} = 5}[/tex]
» Dividing both of the sides of the equation by 8, we get:
- [tex]\rm{x^{2} = \dfrac{5}{8}}[/tex]
» Now take the square root of both the sides of the equation:
- [tex]\rm{x = \sqrt{\dfrac{5}{8}}}[/tex]
- [tex]\rm{x = \dfrac{\sqrt{5}}{\sqrt{8}}}[/tex]
» Rationalize the denominator:
- [tex]\rm{x = \dfrac{\sqrt{5}}{2\sqrt{2}}}[/tex]
- [tex]\rm{x = \dfrac{\sqrt{5} \sqrt{2}}{2(\sqrt{2})^{2}}}[/tex]
- [tex]\rm{x = \dfrac{\sqrt{5} \sqrt{2}}{2 × 2}}[/tex]
- [tex]\rm{x = \dfrac{\sqrt{10}}{4}, -\dfrac{\sqrt{10}}{4}}[/tex]
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