Question

If $a$ represents integers not satisfying $\frac{5x-1}{x^2+3}<1$, then $\sum a_i^2$ is

• A. $30$
• B. $40$
• C. $20$
• D. $10$

Answer 1

The correct option is A $30$

given inequality is $\frac{5x-1}{x^2+3}<1$

if x does not satisfy this inequality, then $\frac{5x-1}{x^2+3}\ge 1$

$x^2+3>0$ So, the inequality becomes $5x-1\ge x^2+3$

$x^2+3-5x+1=x^2-5x+4=(x-4)(x-1)\le 0$

when $x>1,(x-1)>0$ and when $x<4,x-4<0$

So,$(x-4)(x-1)\le 0$

integers in this region are $1,2,3,4$

sum of squares of these integers is $30$