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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-A. 88B. 112C. 144D. 154 |
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Answer» Correct Answer - D `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` |
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