5 second challenge

Algebra Level pending

A = [ 123 x 789 ] B = [ 101 112 131 415 161 718 192 21 222 ] C = [ 324 252 627 ] I f A B C = [ 0 ] , f i n d ⌊ x ⌋ . A=\begin{bmatrix} 123 & x & 789 \end{bmatrix}\\ \\ B=\begin{bmatrix} 101 & 112 & 131 \\ 415 & 161 & 718 \\ 192 & 21 & 222 \end{bmatrix}\\ \\ C=\begin{bmatrix} 324 \\ 252 \\ 627 \end{bmatrix}\\ \\ If\quad ABC=[0],\quad find\quad \left\lfloor x \right\rfloor .

456 -289 0 289

Akshay Sreenivasan by Akshay Sreenivasan , 23, India

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1 solution

O n e x p a n d i n g A B C w e g e t a n e q u a t i o n o f t h e f o r m a x + b = 0 , w h e r e a a n d b a r e p o s i t i v e n u m b e r s . T h i s i m p l i e s x = − ( b a ) . T h e r e f o r e x i s a n e g a t i v e n u m b e r . T h e o n l y n e g a t i v e c h o i c e i s − 289. S o l v i n g t h e a c t u a l e q u a t i o n y i e l d s t h e r e s u l t x = − 288.9888. ⌊ x ⌋ = ⌊ − 288.9888 ⌋ = − 289. On\quad expanding\quad ABC\quad we\quad get\quad an\quad equation\quad of\quad the\quad form\quad ax+b=0,\\ where\quad a\quad and\quad b\quad are\quad positive\quad numbers.\quad This\quad implies\quad x=-(\frac { b }{ a } ).\\ Therefore\quad x\quad is\quad a\quad negative\quad number.\quad The\quad only\quad negative\quad choice\quad is\\ -289.\quad Solving\quad the\quad actual\quad equation\quad yields\quad the\quad result\quad x=-288.9888.\\ \left\lfloor x \right\rfloor =\left\lfloor -288.9888 \right\rfloor =-289.

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