Algebra and Applications Test 3

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Question : 22 of 25

Marks: +1, -0

If

(a^2 + b^2 ) ^3 = (a^3 + b^3 )^ 2

, then

a/b+b/a

is

$1/3$
$2/3$
$-1/3$
$-2/3$

Solution:

(a^2 + b^2 ) 3 = (a^3 + b^3 )^ 2

(a^2 ) ^3 + (b^2 )^ 3 + 3a^2 b^2 (a^2 + b^2 )

= (a^3 )^ 2 + (b^3 )^ 2 + 2a^3 b^3

a^6 + b^6 + 3a^4 b^2 + 3a^2 b^4

= a^6 + b^6 + 2a^3 b^3

3a^2 b^2 (a^2 + b^2 ) = 2a^3 b^3

a^2+b^2={2a^3b^3}/{3a^2b^2}=2/3ab

Then

a/b+b/a={a^2+b^2}/{ab}

={2/3ab}/{ab}=2/3

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