Question

a+1/a=7 then a-1/a=?

Answer 1

@
Given
a+1/a = 7

To find a-1/a

Solution

✏ We know that

✏ (a + b)² = a² + b² + 2ab

✏ (a + 1/a)² = a² + (1/a)² + 2 × a × 1/a

✏ (7)² = a² + 1/a² + 2

✏ 49 = a² + 1/a² + 2

✏ 49 - 2 = a² + 1/a²

✏ 47 = a² + 1/a²

Now,

✏ ( a - 1/a )² = a² + (1/a)² - 2 × a × 1/a

✏ ( a - 1/a )² = a² + 1/a² - 2

✏ ( a - 1/a )² = 47 - 2

✏ ( a - 1/a )² = 45

✏ a - 1/a = √45 or 3√5

@:-)