Question

If `|bar("a")|` = 2, `|bar("b")|` = 5, and `bar("a")*bar("b")` = 8 then `|bar("a") - bar("b")|` = ______ 

Options

• 13

• 12

• `sqrt(13)`

• `sqrt(21)`

Answer 1

`bb(sqrt(13))`

Explanation:

`|bar("a") - bar("b")|^2 = (bar("a") - bar("b")).(bar("a") - bar("b"))` 

= `bar"a".bar"a"-bar"a".bar"b"-bar"b".bar"a"+bar"b".bar"b"`  

= `|bar"a"|^2-2(bar"a".bar"b")+13/2`

= 4 - 16 + 25

`|bar("a") - bar("b")| = 13 = (sqrt13)^2`

∴ `|bar("a") - bar("b")| = sqrt13`