(b) In a two-digit natural number, the digits differ by 1. The product of the number and number obtained by reversing the digits is 252. Find the number.
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Answered by
0
Answer:
12
Step-by-step explanation:
252 factors = 2×2×3×7×3
the product of reverse of the number with differ 1 is 12,21 (21×12=252)
Answered by
1
Let the digit @ tens place = X
Let digit & units place = Y
First Equation:( given)
X - Y = 1
Second Equation :
( 10 X + Y ) ( 10 Y + X ) = 252
Place X = Y + 1, in second equation
( 10 Y + 10 + Y ) ( 10 Y + Y + 1 ) = 252
( 11 Y + 10 ) ( 11 Y + 1 ) = 252
121 Y^2 + 11 Y + 110 Y + 10 = 252
121 Y^2 + 121 Y- 242 = 0
Divide by 121
Y^2 + Y - 2 = 0
Y^2 + 2 Y - Y -2 = 0
Y ( Y + 2 ) -1 ( Y + 2) = 0
So, Y = 1, -2
It can’t be negative number
So Y = 1, X = 2
So, Number = 21
Let digit & units place = Y
First Equation:( given)
X - Y = 1
Second Equation :
( 10 X + Y ) ( 10 Y + X ) = 252
Place X = Y + 1, in second equation
( 10 Y + 10 + Y ) ( 10 Y + Y + 1 ) = 252
( 11 Y + 10 ) ( 11 Y + 1 ) = 252
121 Y^2 + 11 Y + 110 Y + 10 = 252
121 Y^2 + 121 Y- 242 = 0
Divide by 121
Y^2 + Y - 2 = 0
Y^2 + 2 Y - Y -2 = 0
Y ( Y + 2 ) -1 ( Y + 2) = 0
So, Y = 1, -2
It can’t be negative number
So Y = 1, X = 2
So, Number = 21
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