Polynomial Apocalypse.. :D

Algebra Level 4

This problem can be solved easily.. :D provide your answer up to 3 decimal places.. :)


The answer is 402.6058.

View wiki
Mark Vincent Mamigo by Mark Vincent Mamigo , 24, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Dec 28, 2014

x = 1 1 a + 1 b + 1 c + . . . + 1 j = 1 b c d e f g h i j + a c d e f g h i j + a b d e f g h i j + . . . + a b c d e f g h i a b c d e f g h i j x = \dfrac {1}{\frac {1}{a}+\frac {1}{b}+\frac {1}{c}+...+\frac {1}{j}} =\dfrac {1}{\frac {bcdefghij+acdefghij+abdefghij+... +abcdefghi}{abcdefghij}}

= a b c d e f g h i j b c d e f g h i j + a c d e f g h i j + a b d e f g h i j + . . . + a b c d e f g h i \quad = \dfrac {abcdefghij} {bcdefghij+acdefghij+abdefghij+... +abcdefghi}

Using Vieta's Formulas, we have:

⇒ x = 2468 − 123 ⇒ x 2 = ( 2468 − 123 ) 2 = 402.606 \Rightarrow x = \dfrac {2468}{-123} \quad \Rightarrow x^2 = \left( \dfrac {2468}{-123} \right)^2 = \boxed{402.606}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...