[/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="3.22.4" 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="4.3.4"]C.M.I (Chennai mathematical institute ) U.G-2019
Excursion in Mathematics by Bhaskaracharya Pratisthana[/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" inline_fonts="Aclonica"]
It is of the the form of
.
Do you observe ?
where a=\(2^x\)
b=\(3^x\)
\(\frac{a^3+b^3+a^2b+b^2a}{a^2b+b^2a}\)=\(\frac{13}{6}\) \(\Rightarrow\frac{a^2+b^2}{ab}=\frac{13}{6}\) \(\frac{a}{b}+\frac{b}{a}=\frac{13}{6}\) let x=a/b then it is a quadratic equation
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.22.7"]\(6x^2-13x+6=0\) on solving we get x=3/2 or 2/3 now replace x by a/b
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.22.7"]so again putting value of a and b we get final ans is +1 and -1
[/et_pb_tab][/et_pb_tabs][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" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" inline_fonts="Aclonica"]Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.
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