Question

A two digit positive number is such that the product of its digit is 6 .
If 9 is added to the number , the digits interchange their places .
Find the number .

Chapter -> Quadratic Equation class 10 .

PLZ HELP !!!

Answer 1

let the ones digit be x and the tens digit b y
so given:xy=6
and the number=10x+y
10x+y+9=10y+x
9x-9y=-9
x-y=-1
since xy=6
y=6/x
x-6/x=-1
x²-6=-x
so x =2 or -3
so y =2
there for the number is equal to 23

Answer 2

Let the two digit number be 10x+ y or xy in digit form.

So x*y =6.

If 9 is added, digits are interchanged.

10x+ y +9= 10y + x

9= 9y-9x

y -x =1

x-y = -1

(x+y)²=(x-y)²+4xy

=-1²+4(6)

=25

(x+y)=√25=5

Now,

x + y = 5

x - y = -1

========

2x =4

x = 2

from x +y = 5, y =3

So, Hence the number is 20+3 =23

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23+9=32 digits are interchanged.

2*3=6.