Question

If the average of x2 and X is ten, what is the value

Answer 1

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,

`A=(x^2+x)/(2)\ldots\ldots.(1)`

Put A=10 and find value of x.

`\begin{gathered} 10=(x^2+x)/(2) \\ 10*2=x^2+x \\ 20=x^2+x \\ x^2+x-20=0\text{ } \end{gathered}`
`\begin{gathered} x^2-4x+5x-4*5=0 \\ x\mleft(x-4\mright)+5\mleft(x-4\mright)=0 \\ (x-4)(x+5)=0 \end{gathered}`

Hence,

`\begin{gathered} x-4=0 \\ x=4 \\ or \\ x+5=0 \\ x=-5 \end{gathered}`

Now, put x=4 in equation (1).

`\begin{gathered} A=(4^2+4)/(2) \\ A=(16+4)/(2) \\ A=(20)/(2) \\ A=10 \end{gathered}`

Put x=-5 in equation (1).

`\begin{gathered} A=((-5)^2-5)/(2) \\ A=(25-5)/(2) \\ A=10 \end{gathered}`

Hence, x=-5 or 4.