Question

your close frien who happens to be your classmate in school asserted that 2xsquered-4 and 2x squered+4 have the same factor.doyou think your close friend is correct?if not prove it

Answer 1

Given:

Given expressions are

$2x^2-4$ and $2x^2+4$

To find:

We need to find whether the given expressions have same factors or not and tell whether your close friend is correct or not.

Solution:

Before solving the question, we should know the meaning of factors.

Factors are the numbers or expressions which divides another number without leaving any remainder (0).

To find factors of any expression, equate it with zero (0).

Let us find the factors of $2x^2-4$.

$\Rightarrow 2x^2-4=0$

Taking 2 as common,

$\Rightarrow 2(x^2-2)=0$

$\Rightarrow x^2-2=0$

$\Rightarrow x^2=2$

Taking square root on both sides,

$\Rightarrow \sqrt{x^2} =\sqrt{2}$

$\Rightarrow|x|=\sqrt{2}$

$\Rightarrow x=\pm\sqrt{2}$

$\Rightarrow x=\sqrt{2} ,-\sqrt2$

So, the factors of $2x^2-4$ are $x=\sqrt{2} ,-\sqrt2$.

Now, find the factors of $2x^2+4$.

$\Rightarrow 2x^2+4=0$

Taking 2 as common,

$\Rightarrow 2(x^2+2)=0$

$\Rightarrow x^2+2=0$

$\Rightarrow x^2=-2$

Taking square root on both sides,

$\Rightarrow \sqrt{x^2} =\sqrt{-2}$

But square root of negative numbers does not exist.

So, $2x^2+4$ does not have any factors.

From the above answer, it is clear that, both expressions does not have same factors.

Therefore, your close friend answer is wrong. Both expressions does not have same factors.