Question

The average of non zero number and its square is 5 times the number the number is

Answer 1

Let the number be x ∴ its square is x²

Average = ( x + x²)/2

According to question Average of number and its square is 5 times the number

∴ ( x + x²)/2 = 5x

x + x² = 10x

x² = 9x

Dividing both sides by x

x = 9

∴ Desired number is 9

Answer 2

Answer:  The required number is 9.

Step-by-step explanation:  Given that the average of a non zero number and its square is 5 times the number.

We are to find the number.

Let x denote the required number.

Then, according to the given information, we have

$\dfrac{x+x^2}{2}=5\times x\\\\\\\Rightarrow x+x^2=10x\\\\\Rightarrow x^2+x-10x=0\\\\\Rightarrow x^2-9x=0\\\\\Rightarrow x(x-9)=0\\\\\Rightarrow x=0,~~~~~x-9=0\\\\\Rightarrow x=0,~9.$

Since the given number is non zero, so we get

x = 9.

Thus, the required number is 9.