Powers and Roots Practice Test 4

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Question : 39 of 40

Marks: +1, -0

If

a^2+b^2=45

and

ab = 18

, what is

1/a+1/b

?

$±1/3$
$±2/3$
$±1/2$
Cannot be determined

Solution:

a^2+b^2=45

and

ab = 18

(a+b)^2=a^2+b^2+2ab

a^2+b^2=(a+b)^2-2ab

45=(a+b)^2-2×18

45+36=(a+b)^2

a+b=√81=9

Now the value of

1/a+1/b={a+b}/{a b}

=9/18=±1/2

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