Question

a= 2root +1 find a-1/a​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

A = ✓2 + 1

Therefore,

1/A = 1/✓2+1

Rationalizing the denominator ✓2+1 we get,

1/A = 1/✓2 +1 × ✓2-1/ ✓2-1 = (✓2-1)/(✓2+1)(✓2-1) = (✓2-1)/(✓2)² - (1)²

1/A = (✓2-1)/2-1 = ✓2-1

Therefore,

A - 1/A = (✓2+1) - (✓2-1) = ✓2 +1 - ✓2 + 1 = 2

(A-1/A)² = (2)² = 4

Hence,

(A-1/A)² = 4

 

Answer 2

Step-by-step explanation:

a-1/a

=root2+1+ 1/root2+1

=2+2root2+2/root2+1

=2(2+root2)/root2+1

=2root2(1+root2)/1+root2

=2root2 ANSWER