Question

Is √x² = ± x ?

Support your answer with good explanation .

Answer 1

Hi friend
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Your answer
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Is √x² = +- x

Now,
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(-x) × (-x) = x² [ Because x has even exponent]

Also,

x × x = x²

So,
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The value of √x² can be either x or (-x).

That is why,
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√x² = +-x

(proved)

HOPE IT HELPS

Answer 2

Hi there !!

Yes ,

✓x² = +_ x

Method :

We know the square root of a number say ' n' in exponential form is
${n}^{ \frac{1}{2} }$
So,
we here have ✓x²
Since the power of x is 2 and ✓ in exponential for is n^1/2

✓x² can be written as

$\sqrt{ {x}^{2} } = { {x}^{ \frac{1}{2} } }^{ \times 2}$
since the power of 2 in both , the numerator and the denominator is 1 , it can be simplified using the law of exponents, ie , a^m/b^m = (a/b)^m but in this case, a and b are equal

So,

${x}^{ {( \frac{2}{2} } ) {}^{1} }$

$= {x}^{1} = {x}$
Hence √x² = ± x

If we take the negative sign of x ,
then,

-x^ 1/2×2,

both the 2's in the numerator and the denominator will be 1 by using the above law of exponent
and we will be left with -x

Hence,
it is proved that

✓x² = +_ x