if (2+x/2)^5 + (2-x/2)^5 = a + bx^2 + cx^4, then b/a + 4c = ?

Question

just a doubt please help because i am kinda stupid and also i dont really need any description but alright i guess

Answer 1

it's a little tedious in calculations, but b/a +4c = 40/64+4(5/8) = 3.125 = 3 1/8 = 25/8

if you add (2+x/2)^5 to (2-x/2)^5 half the terms, the odd powered x terms, cancel out

leaving

2^5 +40x^2 +(5/8)x^4 =a +bx^2 +cx^4

with a= 64, b= 40, c= 5/8

use the formula: (a+b)^5 = a^5 +5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^4 with a=2, b=x/2 and b=-x/2 for the 2nd expression.