If X : Y = 7 : 3 then the value of \(\frac{X^2+Y^2}{X^2-Y^2}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{29}{20}\)
Since \(X:Y=7:3\), take \(X=7k\) and \(Y=3k\). Every term of the fraction then carries \(k^2\), which cancels, so the numbers 7 and 3 can be used directly.
Numerator: \(X^2+Y^2=49+9=58\)
Denominator: \(X^2-Y^2=49-9=40\)
Value of the fraction: \(\displaystyle \frac{58}{40}=\frac{29}{20}\)