Alliteration of Numbers!

Algebra Level 3

x + 19 x + 10 = ( 2 x + 33 2 x + 24 ) 2 \large \frac {x+19}{x+10} = \left(\frac{2x + 33}{2x + 24}\right)^2

Find the value of x x satisfying the equation above.

7 4 6 8 11

Nibedan Mukherjee by nibedan mukherjee , 25, USA

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1 solution

Sam Bealing
Jun 30, 2016

( 2 x + 24 ) 2 ( x + 19 ) = ( 2 x + 33 ) 2 ( x + 10 ) (2x+24)^2 (x+19)=(2x+33)^2 (x+10) ( 4 x 2 + 96 x + 2 4 2 ) ( x + 19 ) = ( 4 x 2 + 66 x + 3 3 2 ) ( x + 10 ) \left (4x^2+96x+24^2 \right)(x+19)=\left (4x^2+66x+33^2 \right )(x+10) 4 x 3 + 172 x 2 + 2400 x + 10944 = 4 x 3 + 172 x 2 + 2409 x + 10890 4x^3+172x^2+2400x+10944=4x^3+172x^2+2409x+10890 54 = 9 x ⟹ x = 6 54=9x \implies \boxed{\boxed{x=6}}

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Moderator note:

Simple standard approach.

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