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F(x)=e^x+e^-x prove f(x+y)=f(x-y)=f(2x)+f(2y)

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97 cents Livingston
Answer:

 \huge\star{\red{Q}{uestion}}\star\:

Sum of the digits of a two-digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the given

number.

 \huge\star{\red {A}{nswer}}\star\:

 \huge\underline {Let,}

The tens digit of the required number be x

and the units digit be y

 \huge\underline {Then,}

x + y = 12 ......... eq. (1)

Required number = (10x + y)

Number obtained on reversing the digits = (10y + x)

 \huge\underline {Therefore,}

(10y + x) - (10x + y) = 18

9y - 9x = 18

x - y = 12 ......... eq. (2)<br>

On adding eq. (1) and eq. (2)

 \huge\underline {We\: get}

x + y + y - x = 12 +2

2y = 14

y = 2

 \huge\underline {Therefore}

x = 5

Hence, the required number is 57

 \huge\green { Hope\: this\: helps\: you}

 \huge\red {\mathtt{@SpammingKing\: here}}

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Livingston
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