Distance between Two Points on the Same Coordinate Axes
Let x and y b...
Question
Let x and y be two 2- digit number such that y is obtain by reversing the digits of x.suppose they also satisfy x2−y2=m2 for some positive integer m. The value of x+y+m is.
A
88
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B
112
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C
144
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D
154
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Solution
The correct option is D 154 X→ab or x=10a+b y→ba or y=10b+a Now x2−y2=(10a+b)2−(10b+a)2 =99(a2−b2) =32×11(a+b)(a−b)..........(1) According of Q (a+b)(a−b)=11 and a−b=1 ⇒a+b=11 and a−b=1 ⇒a=6,b=5 Hence x=65 y=56 and m=33 ⇒x+y+m=154