There are two numbers.
The avergae of numbers, A=10
The average of a set of terms is the sum of terms divided by the number of terms.
Hence, the average of the given numbers is,
[tex]A=\frac{x^2+x}{2}\ldots\ldots.(1)[/tex]Put A=10 and find value of x.
[tex]\begin{gathered} 10=\frac{x^2+x}{2} \\ 10\times2=x^2+x \\ 20=x^2+x \\ x^2+x-20=0\text{ } \end{gathered}[/tex][tex]\begin{gathered} x^2-4x+5x-4\times5=0 \\ x\mleft(x-4\mright)+5\mleft(x-4\mright)=0 \\ (x-4)(x+5)=0 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x-4=0 \\ x=4 \\ or \\ x+5=0 \\ x=-5 \end{gathered}[/tex]Now, put x=4 in equation (1).
[tex]\begin{gathered} A=\frac{4^2+4}{2} \\ A=\frac{16+4}{2} \\ A=\frac{20}{2} \\ A=10 \end{gathered}[/tex]Put x=-5 in equation (1).
[tex]\begin{gathered} A=\frac{(-5)^2-5}{2} \\ A=\frac{25-5}{2} \\ A=10 \end{gathered}[/tex]Hence, x=-5 or 4.
