Question

pls solve this question
I will give you 50 points for this question.​

Answer 1

Answer:

Option c

Step-by-step explanation:

Let (x - 1)(x + 2) = m

Now, we know that,

(√a) × (√a) = a

For example,

(√5) × (√5) = 5

Then,

Here we have,

√[(x - 1)(x + 1)] × √[(x - 1)(x + 2)] × √[(x - 1)(x + 2)]

= √[(x - 1)(x + 1)] × (√m) × (√m)

= √[(x - 1)(x + 1)] × m

Let's just divide the Question into two,

So, we get m as a part of the answer,

Now,

m = (x - 1)(x + 2)

= x² + 2x - x - 2

= x² - x - 2

So, it's degree will be 2, as x² has the highest power among all.

Back to the 1st part of the answer,

√(x - 1)(x + 1)

= √x² - x + x - 1

= √x² - 1

Let's say this number has a square root, then the only possible value of x² will be x² = 1

All the other values will either given a non perfect square or an imaginary number.

So,

If x² = 1

Then,

√x² - 1 = √1 - 1

= √0

= 0

Hence, From the original Question,

√[(x - 1)(x + 1)] × √[(x - 1)(x + 2)] × √[(x - 1)(x + 2)]

We get, IF x² = 1 then,

= 0 × (x² - x - 2)

= 0

But zero can also be written as,

0 × 1 = 0 × x⁰

So,

Highest power of x will be 0 and degree of the polynomial becomes 0

But, 0 is not an option.

Which means x² ≠ 1

And. we can say that options b and d is wrong.

So, the only possible is a or c.

Then, we know that no matter what positive values x² takes, x will always be a non perfect square number.

That is,

√x² - 1 will always give a number that is not a rational number. You wouldn't have understood it.

Simply speaking,

√x² - 1 will be equal to √2, √3, √5, √6, etc, that is, non perfect squares.

And since 2 is also not an option because x² - x - 2 has a degree of 2, Option c must be correct.

Because if it is not defined, that means it is not a polynomial, So Option C has to be correct.

Hope it helped you and believing you understood it...All the best

Answer 2

Answer:

option D is correct

I hope it's helpful you