If x= 3 4 8 + 3 5 4 8 12 + 3 5 7 4 8 12 16 + , then 2 x^2+5 x=

Step-by-step solution

x= 3 4 8 + 3 5 4 8 12 + 3 5 7 4 8 12 16 + Let, aligned (1+y)^n=1+n y+ & n(n-1) 2 ! y^2+ n(n-1)(n-2) 3 ! & + n(n-1)(n-2)(n-3) 4 ! y^4+ . . aligned If we compare with third term on words, the aligned n(n-1) 2 ! y^2 & = 3 4.8 , n(n-1)(n-2) n ! y^3 & = 3 5 4 8 12 aligned and n(n-1)(n-2)(n-3) 4 ! y^4= 3 5 7 4 8 12 16 On solving, we are getting. So, aligned & x=(1+y)^n-1-n y= (1- 1 2 )^ -1 / 2 -1- (- 1 2 ) ( -1 2 ) & 2 -1- 1 4 = 2 - 5 4 & Now, 2 x^2=2 [2+ 25 16 - 5 2 ]=4+ 25 8 -5 2 & and 5 x=5 2 - 25 4 & aligned So, alig