Question

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

Answer 1

Answer:

5/14.

Step-by-step explanation:

Cross-multiplying the ratio, we get:

5a - 5b = a + b

So, 4a = 6b, or 2a = 3b.

Or, $b = \frac{2a}{3}$

Now, $a^2 - b^2 = a^2 - \frac{4a^2}{9}$

$= \frac{5a^2}{9}$

Similarly, $a^2 + b^2 = \frac{14a^2}{9}$

Dividing, we get: $\frac{a^2 - b^2}{a^2 + b^2} = \frac{\frac{5a^2}{9}}{\frac{14a^2}{9}} = \frac{5}{14}$

Answer 2

Answer:

(a^2-b^2) ÷ (a^2+b^2) = 5:13

Step-by-step explanation:

(a+b) / (a-b) = 1/ 5

Cross Multiplication

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

5a + 5b = a-b

5a-a + 5b + b = 0

4a + 6b = 0

4a = -6b

a/b = -6/4

a/b = -3/2

Squaring both the sides

(a/b)^2 = (-3/2)^2

a^2/b^2 = 9/4

By Componendo & Dividendo Property

(a^2-b^2) / (a^2+b^2) = 9-4/9+5

(a^2-b^2) / (a^2+b^2) = 5/13