Question

q1.if we add the square of the digit in the tens place of a positive two-digit number to the product of the digits of that number we shall get 52 and if we add the square of the digit in the units place to the same product of the digits we shall get 117. find the two-digit number.

Answer 1

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Answer 2

Answer:

49

Step-by-step explanation:

Let n(a,b) be two digit number

n(a,b)=10a+b

(square of of digits in ten’s place)+(product of digits)=2

a²+ab=52→(1)

(square of digit in unit place)+(product of digits)=117

b²+ab=117→(2)

(1)+(2)⇒(a+b)²

=169

∴a+b=13(∵a≥1,b≥0)

(1)−(2)⇒a²−b²

=65

−a−b=−5

a=4,b=9

∴n(a,b)=49  is the required number.

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