Question

In a two digit natural number. the digit at the tense place is equal to the square of the digit at units place. If 18 is substracted from the number, the digit get interchanged. find the number.
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Answer 1

ANSWER: 42

solution;

Let the unit digit be x

ten's digit = x²

Number = 10×x²+x

= x(10x+1)

After Interchange of digits

New Number = 10×x+x²

= x(10+x)

According to condition,

x(10x+1)-18 = x(10+x)

10x²+x-18 = 10x+x²

10x²-x²+x-10x-18 = 0

9x²-9x-18 = 0

9 (x²-x-2) = 0

x²-x-2 = 0

x²-2x+x-2 = 0

x(x-2)+1(x-2) = 0

(x-2)×(x+1) = 0

x-2 = 0

x= 2

Number = x(10x+1)

= 2(10×2+1)

= 2(20+1)

= 2(21) = 42

HOPE THIS IS HELPFUL!