Dividing And Expressing Factorials

Number Theory Level 1

x ! = 11 ! + 10 ! 9 ! \large x! =\dfrac{11! + 10!}{9!}

Find the value of x x satisfying the equation above.

Notation :

! ! denotes factorial . For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 5.

View wiki
Ash R by Ash R , 16, USA

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.

2 solutions

Rohit Udaiwal
Apr 6, 2016

11 ! + 10 ! 9 ! = x ! 9 ! ( 10 ⋅ 11 + 10 ) 9 ! = x ! 120 = x ! 5 ! = x ! ∴ x = 5 \begin{aligned}\dfrac{11! + 10!}{\color{#3D99F6}{9!}} = & x! \\ \dfrac{\color{#3D99F6}{9!}(10\cdot11+10)}{\color{#3D99F6}{9!}}= & x! \\ 120= & x! \\ 5!= & x! \\ \therefore \color{#20A900}{x= 5} \end{aligned}

14 Helpful 0 Interesting 0 Brilliant 0 Confused

My approch is same yours!! :-)

akash patalwanshi - 5 years, 2 months ago
Atul Kumar Ashish
Apr 15, 2016

x ! = 11 ! + 10 ! 9 ! x!=\frac{11!+10!}{9!}
x ! = 9 ! 10 ( 11 + 1 ) 9 ! x!=\frac{9!10(11+1)}{9!}
x ! = 10 • 12 x!=10•12
x ! = 1 • 2 • 3 • 4 • 5 x!=1•2•3•4•5
x ! = 5 ! x!=5!
x = 5 \boxed{x=5}



0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...