Question : If $x:y=2:1$, then $(x^{2}-y^{2}) : (x^{2}+y^{2})$ is:
Option 1: 3 : 5
Option 2: 5 : 3
Option 3: 4 : 5
Option 4: 5 : 6
Answer (1)
25th Jan, 2024
Correct Answer: 3 : 5
Solution :
$x : y = 2 : 1$
Let $x = 2k$ and $y = k$
So, $x^2 = 4k^2$ and $y^2 = k^2$
Now putting the value in the given equation, we get,
$(x^{2}-y^{2}) : (x^{2}+y^{2})$
$= (4k^2 - k^2) : (4k^2 + k^2)$
$= 3k^2 : 5k^2=3:5$
Hence, the correct answer is 3 : 5.
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