Question

determine by substitution if -3 is the root of x²=5​

Answer 1

Answer:

No -3 is not the root of x²=5

Step-by-step explanation:

By substitution, (-3)² = 9

Now, x²=9

But also x²=5 which is not satisfying

Answer 2

Answer:

No, -3 is not a root of $x^2=5$.

Step-by-step explanation:

Replacing x with -3 gives us: $(-3)^2=5$.

Why the parentheses?

The parentheses are necessary to make sure we are squaring the negative sign as well. Otherwise, we will only be squaring the 3 and then attaching the negative sign after squaring.

To demonstrate: $-3^{2} =-(3^2)=-(3\times3)=-9$ but $(-3)^2=(-3)\times(-3)=9$ since a negative multiplied by a negative gives a positive result

Back to the question:

Simplifying each side gives us $9=5$ which is clearly false.

A root is a value of the variable used to make the equation true.

So, since $x=-3$ does NOT make the equation true, it is NOT a root.

Let me know if you have any questions! Hope that helped! :)