Statement 1: If √12 - √8 = a, then √12 + √8 is equal to 4/a. Statement 2: a + √b is called the rationalizing factor of c + √d if their product is 1.

• Statement 1 is true; Statement 2 is true; Statement 2 is the correct explanation of Statement 1.

• Statement 1 is true; Statement 2 is true; 2 is not the correct explanation of Statement 1.

• Statement 1 is true; Statement 2 is false.

• Statement 1 is false; Statement 2 is true.

It is an assertion-reasoning question. Please help me to solve this. Need step-by-step explanation as well. Thank you.

Statement 1 is true; Statement 2 is false.

Step-by-step explanation:

Statement 1:

√12 - √8 = a

Let's use the given value of √12 + √8 ,that is, 4/ a.

If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:

=> (√12- √8)(√12 + √8) = a × 4/a

On the LHS,

identity used:

(a-b)(a+b) = a²-b²

On the RHS:

a gets canceled due to its presence in both the numerator as well as the denominator.

=> 12 - 8 = 4

=> 4 = 4

That's it!

We got LHS = RHS, that approves the existence of the given statement.

Statement 2:

"a + √b is called the rationalizing factor of c + √d if their product is 1"

That's not entirely right!

The correct statement would be:

" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."

Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.

Hence, I'd say:

Statement 1 is correct but Statement 2 isn't.

That's the third option.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.