(a) 164. (b)172. (c)192. (d)194. (e)212
[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version="3.25"][et_pb_column type="4_4" _builder_version="3.25" custom_padding="|||" custom_padding__hover="|||"][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="4.0" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="4.0"]American Mathematical Contest 2007 10 A Problem 20
[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="4.0" open="off"]Basic Algebra
[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.0" open="off"]4/10
[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.0" open="off"]Challenges and Thrills in Pre College MathematicsExcursion Of Mathematics
[/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]Step 1.Look's hard , lets see we are given with \(a\)+\(\frac{1}{a}\)=\(4\) and we need to find \(a^4\)+\(\frac{1}{a^4}\). So first we will square both sides in order to get \(a^2\)+\(\frac{1}{a^2}\) and find its value. Give it a try!!!!.
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="4.0"]Step 2.We reached the power 2 now aim is to get to power 4. Now After getting the the value of \(a^2\)+\(\frac{1}{a^2}\) , again square both sides to get the value of the expression \(a^4\)+\(\frac{1}{a^4}\) . Very close to the solution !!!!!!.
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="4.0"]Step 3 .Now we get the equation \(a^4\)+\(\frac{1}{a^4}\) after solving \((a^2+\frac{1}{a^2})^2\). Now I hope u can see the answer by your self just a last step!!!!.
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="4.0"]Step 4By solving we get the results that is \(a^2\)+\(\frac{1}{a^2}\)=14
and \(a^4\)+\(\frac{1}{a^4}\) =194 which is our required value to find ,thats it!!!
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