Integral values of an expression

manpreet Best Answer 2 years ago

Let b=a2+5a+8−−−−−−−−−√−a2−3a+4−−−−−−−−−√b=a2+5a+8−a2−3a+4

Find number of integral values of b.

My longlong way using Calculus :

Find domain of function : RR

Note that function is continuous

Prove the function is always increasing

Find limit as x−>∞x−>∞ and x−>−∞x−>−∞

Get it as −4−4 and 44

Conclude that only possible integral values are −3,−2,−1,0,1,2,3−3,−2,−1,0,1,2,3.

But I am not happy as that is too long for a 3 marker question (in my exam)

I want nice way perhaps using theory of quadratic expressions?

EDIT Well you guys gave a short proof using calculus but I wanted to see a proof without using calculus as it was not in the syllabus of the test. And I have definitely not studied about asymptotes in detail (only in hyperbola briefly)

Both of the b.com/tag/answers">answers are excellent.