19that would complicate things...there is some simpler route, ifeel !...lets think !...i was also going for the method, advised by qwerty !
Solve for x :
(x+3)^{5}-(x-1)^{5}\geq 244
PS: the ans given is
x \in (-infinity,-2] U [0,infinity)
i thought of solving by taking x +1 = y ...so dat we can get some symmetry ...but ans nahi match hora ....pls see f any 1 can get the ans
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5 Answers
19
62Qwerty you were doing the right things.
y=x+1
(y+2)5-(y-2)5>=244
2 {5.y4.2+10.y2.23+25}>=244
{5.y4+10.y2.22+24}>=61
5.y4+10.y2.22>=45
y4+8.y2-9>=0
(y2-1)(y2-9) >=0
now I am sure you can finish it off [1]
341I thought that in this strongly graphing community, this prob would have been solved with a picture
if you let f(x) = (x+3)5-(x-1)5, we can see that f'(x) = 0 only at x =-1 and f'(x)>0 for x>-1 and <0 for x<-1.
So its shaped like a quadratic symmetric about x = -1. So f(x)≥ f(0) when x≥0. Since f(-2) = f(0), and when x≤-2 too we have f(x)≥f(-2).