How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

# Real numbers problem - C.M.I - U.G - 2019

## Understand the problem

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$\frac{8^x+27^x}{12^x+18^x}=\frac{7}{6}$

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C.M.I (Chennai mathematical institute ) U.G-2019

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### Real Numbers

[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="3.22.4" open="off"]8 out of 10

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It is of the the form of  $\frac{a^3+b^3}{a^2b+b^2a}$ . Do you observe ?  where a=$2^x$ b=$3^x$

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$\frac{a^3+b^3+a^2b+b^2a}{a^2b+b^2a}$=$\frac{13}{6}$ $\Rightarrow\frac{a^2+b^2}{ab}=\frac{13}{6}$ $\frac{a}{b}+\frac{b}{a}=\frac{13}{6}$ let x=a/b then it is a quadratic equation

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$6x^2-13x+6=0$ on solving we get x=3/2 or 2/3 now replace x by a/b

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so again  putting value of a and b we get final ans is +1 and -1

## Connected Program at Cheenta

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.

## Similar Problem

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