Let x and y be two 2-digit numbers such that y is obtained by recersing the digits of x. Suppose they also satisfy `x^(2)-y^(2)=m^(2)` for same positive integer m. The value of x + y + m is-

Options

A. 88
B. 112
C. 144
D. 154

Answer

D

Explanation

`x=ab=10a+b`
`y=ba=10b+a" "1lea, ble9`
`x^(2)-y^(2)=m^(2)`
`100a^(2)+b^(2)+20ab-(100b^(2)+a^(2)+20sb)=m^(2)`
`99(a^(2)-b^(2))=m^(2)`
`9xx11xx(a-b)(a+b)=m^(2)`
m is interger so`" "a=6" "{Note :"a-bne9"(think why ?)"}`
`b=5`
`m^(2)=9xx11xx1xx11rArrm=3xx11`
`x+y+m=10a+b+10b+a+33`
`=11(a+b)+33=11(11)+33=121+33=154`