Math, asked by priyankachaudhary143, 9 months ago

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Answered by Anonymous

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Let the x be the number at units place and y be the number at digits place

number will be = x + 10y

reverse number will be = 10x + y

Product of digit is 20

Therefore, xy = 20 _____(1)

Original number + 9 = reversed number

x + 10y + 9 = 10x + y

9x - 9y = 9

x - y = 1 _____(2)

using formula (x + y)² = (x - y)² + 4xy

(x + y)² = (1)² + 4(20).......[by using equation (1) and (2)]

(x + y)² = 1 + 80 = 81

x + y = 9 _____(3)

solve equation (3) and (2)

x + y = 9

x - y = 1

by adding, we get,

2x = 10

=> x = 5

=> y = 9 - 5 = 4

so x and y are 5 and 4 respectively

number is x + 10y = 5 + 10(4) = 5 + 40 = 45

The required number is 45

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