Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩sin(ax2+bx+c)x2−1,if x<1−1,if x=1a sgn(x+1)cos(2x−2)+bx2,if 1<x≤2 is continuous at x=1, then the value of a2+b25 is ( Here, sgn(k) denotes signum function of k )

Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩s

1.	Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩sin(ax2+bx+c)x2−1,if x<1−1,if x=1a sgn(x+1)cos(2x−2)+bx2,if 1<x≤2 is continuous at x=1, then the value of a2+b25 is ( Here, sgn(k) denotes signum function of k )
Answer» Let $a, b, c \in R$ such that $a + b + c = π .$ If $f (x) = ⎧ ⎪⎪⎪ ⎨ ⎪⎪⎪ ⎩ \begin{matrix} \frac{sin (a x^{2} + b x + c)}{x^{2} - 1}, & if x < 1 - 1, & if x = 1 a sgn (x + 1) cos (2 x - 2) + b x^{2}, & if 1 < x \leq 2 \end{matrix}$ is continuous at $x = 1,$ then the value of $\frac{a^{2} + b^{2}}{5}$ is ( Here, $sgn (k)$ denotes signum function of $k$ )