1.

Answer the above questions with proper explanation

Answer»

[I already SOLVED 3 no. problem in your previous question. So, I am solving the 4th one only.]

The answer is given below :

Given,

a = 3 - √n, where n is a NATURAL number,
n = 1, 2, 3, ...

To find the least positive value of 'a', we need to put n = 2, so that 'a' BECOMES the least.

When n = 2,

a = 3 - √2

So, the least value of 'a' being 'p', p = 3 - √2

Now,

p = 3 - √2

= 2 - √2 + 1

= (√2)² - (2 × √2 × 1) + (1)²

= (√2 - 1)²

Since, p is positive,

√p = √2 - 1

and

1/√p = 1/(√2 - 1)

= (√2 + 1)/{(√2 - 1)(√2 + 1)},
by rationalising the denominator by multiplying both the NUMERATOR and the denominator by (√2 + 1)

= (√2 + 1), since (√2 - 1)(√2 + 1) = 2 - 1 = 1

Now,

√p + 1/√p

= √2 - 1 + √2 + 1

= 2√2

So, option (1) is correct.

Thank you for your question.


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