In a △ABC, a,b,c are the sides opposite to the angles A,B,C respectively. The corresponding values of sides are a=x2,b=4x2+x−1 and c=x3, where x∈R. If sinA+sinC=2sinB, then x can be expressed as αβ (0<α,β<10). A function is defined as f(t)={k1α+t t>0k2β+t+2 t≤0, where k1,k2 are integers. If the function is continous for all x∈R, then k1+k2 can be equal to

In a △ABC, a,b,c are the sides opposite to the angles A,B,C respecti

1.	In a △ABC, a,b,c are the sides opposite to the angles A,B,C respectively. The corresponding values of sides are a=x2,b=4x2+x−1 and c=x3, where x∈R. If sinA+sinC=2sinB, then x can be expressed as αβ (0<α,β<10). A function is defined as f(t)={k1α+t t>0k2β+t+2 t≤0, where k1,k2 are integers. If the function is continous for all x∈R, then k1+k2 can be equal to
Answer» In a $△ A B C$ , $a, b, c$ are the sides opposite to the angles $A, B, C$ respectively. The corresponding values of sides are $a = x^{2}, b = 4 x^{2} + x - 1$ and $c = \frac{x}{3}$ , where $x \in R$ . If $sin A + sin C = 2 sin B$ , then $x$ can be expressed as $\frac{α}{β} (0 < α, β < 10) .$ A function is defined as $f (t) = {\begin{matrix} k_{1} α + t t > 0 k_{2} β + t + 2 t \leq 0 \end{matrix},$ where $k_{1}, k_{2}$ are integers. If the function is continous for all $x \in R$ , then $k_{1} + k_{2}$ can be equal to