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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)`
Solution
`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`
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