Question

Product of two digit is numer21. if we add 36 to the number, the new number is obtained is a number formed by interchanging of the digits. represent the following situation in the form of quadratic equation.

Answer 1

Answer:

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Step-by-step explanation:

Let the unit digit be 'x'

Let the ten's digit be 'y'.

Original number will be

10\times \text{ten's digit}+one's\ digit\\\\=10x+y

On interchanging of digits,

Let unit's digit be 'y'.

Let ten's digit be 'x'.

New number will be

10\times \text{ten's digit}+one's\ digit\\\\=10y+x

According to question,

Product of digit of two digit number = 21

So, it becomes,

xy=21-----------------------(1)

If we add 36 to the number the new number obtained is number formed by interchange of digits.

10x+y+36=10y+x\\\\10x-x+36=10y-y\\\\9x+36=9y\\\\36=9y-9x\\\\36=9(y-x)\\\\\frac{36}{9}=y-x\\\\4=y-x\\\\y=4+x----------------------------(2)

Put the value of eq(2) in Eq(1).

xy=21\\\\x(4+x)=21\\\\x^2+4x=21\\\\x^2+4x-21=0\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x+7)(x-3)=0\\\\x+7=0,x-3=0\\\\x=-7,x=3

x=-7 will be rejected.

So, x=3 and

xy=21\\\\3y=21\\\\y=\frac{21}{3}\\\\y=7

Hence, original number will be

10x+y=10\times 3+7=30+7=37

New number will be

10y+x=10\times 7+3=70+3=73

Therefore, Numbers are 37 and 73.