Question

Find the square root of
A square/4 +1/ A square - 1/A +A/2- 3/4

Answer 1

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

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