QJEEM23Ma5509: JEE Main 2023 Mathematics - Class 11 JEEM23Ma5509 Solution: Let and . If denotes the greatest integer , then :

Question

Verified Solution • 2025–26 Session moderate

Let

x=(8 \sqrt{3}+13)^{13}

and

y=(7 \sqrt{2}+9)^9

. If

[t]

denotes the greatest integer

\leq t

, then :

Accepted Answer

If ${I_1} + f = {(8\sqrt 3 + 13)^{13}},f' = {(8\sqrt 3 - 13)^{13}}$

${I_1} + f - f'=$ Even

${I_1} =$ Even

${I_2} + f - f' = {(7\sqrt 2 + 9)^9} + {(7\sqrt 2 - 9)^9}$

= Even

${I_2} =$ Even

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