Correct Answer - Option 3 : 2
Given:
\( \frac{{{{\left( {987~+~513} \right)}^2}~+~{{\left( {987~-~513} \right)}^2}}}{{{{\left( {987} \right)}^2}~+~\;{{\left( {513} \right)}^2}}}\)
Concept Used:
(a + b)2 = (a2 + b2 + 2ab) ----(1)
(a - b)2 = (a2 + b2 - 2ab) ----(2)
Calculation:
Adding equation (1) and (2), we get
(a + b)2 + (a - b)2 = 2(a2 + b2)
Where,
a = 987 and b = 513
According to the question,
\(\frac{{{{\left( {987~+~513} \right)}^2}~+~{{\left( {987~-~513} \right)}^2}}}{{{{\left( {987} \right)}^2}~+~\;{{\left( {513} \right)}^2}}}~=~\;\frac{{2[{{\left({987}\right)}^2}\;~+~\;{{\left({513}\right)}^2}]}}{{{{\left[({987}\right)}^2}\;~+~\;{{\left({513}\right)}^2}]}}\)
⇒ 2
∴ The value of \( \frac{{{{\left( {987~+~513} \right)}^2}~+~{{\left( {987~-~513} \right)}^2}}}{{{{\left( {987} \right)}^2}~+~\;{{\left( {513} \right)}^2}}}\) is 2.