Question

a^2+1/a^2 = 27, find only a-1/a

Answer 1

Given

• a² + 1/a² = 27

To find

• a - 1/a

Solution

✮(a-1/a)² = (a²+1/a²)-2

• (a-1/a)² = (27 - 2) = 25

✮Square root on both sides

• √(a-1/a)² = √25
• (a - 1/a) = ±5

∴ If a² + 1/a² = 27, then a - 1/a = ±5