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If (a+b):(a-b) = 1:5, then (a^2 - b^2):(a^2 + b^2) equals to what ?

+1 vote
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If (a+b):(a-b) = 1:5, then (a^2 - b^2):(a^2 + b^2) equals to what ?
posted Sep 3, 2015 by Samardeep Acharya

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2 Answers

+1 vote

(4/9) / (13/9) = 0.386
(a + b) / (a - b) = 1/5
5a + 5b = a - b
b = -4/6 * a
.
a^2 = a^2
b^2 = (-4/6 * a)^2 = (-4/6)^2 * (a)^2 = 4/9 * a^2
.
(a^2 - b^2) / (a^2 + b^2) =
(a^2 - 4/9 * a^2) / (a^2 + 4/9 a^2) =
(5/9 * a^2) / (13/9 * a^2) = (5/9) / (13/9)

answer Sep 3, 2015 by Jcm
0 votes

a+b / a-b = 1/5
a+b+a-b / a+b-a+b = 1+5 / 1-5
a/b = - 3/2

a^2 / b^2 = 9/4
a^2 - b^2 / a^2 + b^2 = 9-4 / 9+4 = 5/13

answer Sep 4, 2015 by Avantika Agrawal



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