If (a + b) : (a - b) = 5 : 3, then (a^2 + b^2 ) : (a^2 - b^2 ) = ?

Algebra and Applications Test 1

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(a + b) : (a - b) = 5 : 3

, then

(a^2 + b^2 ) : (a^2 - b^2 ) = ?

Solution:

{a+b}/{a-b}=5/3

3a + 3b = 5a - 5b

a = 4b

(a^2+b^2):(a^2-b^2)

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

={16b^2+b^2}/{16b^2-b^2}={17b^2}/{15b^2}

= 17 : 15

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