Question

The sum of the digits of a two-digit number is 10 and their product is 16.

Answer 1

Let the digit at the one's place be x. Then, the digit at ten's place = (10 - x)

∴ The Number = 10·(10 - x) + x

                        = 100 - 10x + x

                        = 100 - 9x

According to the question;

   (10 - x)·x = 16

⇒ 10x - x² = 16

⇒ 10x - x² - 16 = 0

⇒ - ( - 10x + x² + 16) = 0

⇒ - 10x + x² + 16 = 0

⇒ x² - 10x + 16 = 0

⇒ x² - 2x - 8x + 16 = 0              [Splitting the Middle Term]

⇒ x·(x - 2) - 8·(x - 2) = 0

⇒ (x - 8) (x - 2) = 0

⇒ x = 8 or x = 2

Therefore, the two digits of the number are = 8 and 2

Answer 2

$\mathfrak{ The\: number\: is\: maybe\: 28\: or\: 82. }$

Step-by-step explanation:

Let the digit at tens place be x.

So, the digit at the unit place be y.

According to the question,

The sum of two digits is 10.

So, x+y=10 --(1)

Also, Their product is 16.

xy=16 --(2)

The simplest way that you'll find to answer this question is by the given way.

From eq. (2),

$y= \frac {16}{x} --(3)$

Putting value of y from (3) in (1)

$\frac{x}{1}+\frac{16}{x}=10\\ \\ \frac{x^2+16}{x}=10\\ \\ x^2+16=10x\\ \\ x^2-10x+16=0\\ \\ x^2-8x-2x+16=0\\ x(x-8) -2(x-8)=0\\ (x-2) (x-8)=0\\ \therefore, x=2\: and\: 8<strong>.</strong>$

Putting x=2 in eq. (1)

2+y=10

y=10-2

y=8

___________________

Putting x=8 in eq. (1)

8+y=10

y=10-8

y=2

So, if x=2 then y= 8; the number would be 28,

and if x=8 then y=2; the number would be 82.