Question

Ma poate ajuta cineva? Multumesc.

Answer 1

A(n;k)=n!/(n-k)!

6)
a) A(x-2; 2)=42⇔(x-2)!/(x-4)!=42⇔(x-4)!(x-3)(x-2)/(x-4)!=42⇔(x-3)(x-2)-42=0⇔x^2−5x−36=0⇔(x+4)(x-9)=0⇒x=9
b) A(x+2; 2)=56(x+2)⇔(x+2)!/x!=56(x+2)⇔x!(x+1)(x+2)/x!=56(x+2)⇔(x+1)(x+2)=56(x+2)⇔x^2−53x−110=0⇔(x+2)(x−55)=0⇒x=55
c) A(x+1; 2)=30⇔(x+1)!/(x-1)!=30⇔(x-1)!x(x+1)/(x-1)!=30⇔x(x+1)=30⇔x^2+x−30=0⇔(x−5)(x+6)=0⇒x=5

2) 
b)(2*3!+3*4!/2!)/5*5!-3!⇔(2*2*3+3*3*4)/(5*2*3*4*5-2*3)⇔48/594=8/99
c)(11!/5!-11!/6!)/(10!/5!-10!/6!)⇔(6*7*8*9*10*11-7*8*9*10*11)/(6*7*8*9*10-7*8*9*10)⇔277200/25200=11