Question

The sum of the squares of two positive integer is 208. if the square of the larger number is 18 times the smaller number find the numbers.

Answer 1

Answer:

Step-by-step explanation:

Given,

• The sum of the squares of two positive integer is 208.
• If the square of the larger number is 18 times the smaller number.

To Find,

• The Numbers.

Solution :-

Let the smaller number be x,

Then,

Square of the larger number = 18x

Square of the smaller number = x²

Sum of the squares of the integers = 208

According to the question,

⇒ x² + 18x = 208

⇒ x² + 18x - 208 = 0

By using prime factorization method, we get

⇒ x² + 26x - 8x - 208 = 0

⇒ x(x + 26) - 8(x + 26) = 0

⇒ (x + 26) (x - 8) = 0

⇒ x + 26 = 0 or x - 8 = 0

⇒ x = - 26, 8 (As x can't be negative)

⇒ x = 8

Square of larger number = 18x = 18 × 8 = 144

Larger number = √144 = 12

Hence, the number are 8 and 12.

Answer 2

Step-by-step explanation:

Have Given :-

• The sum of the two squares is = 208.
• the larger number is 18 times the smaller number.

Solution :-

Let the smaller number be x.

Square of the larger number is = 18x

Square of the smaller number is = x²

According to the question :-

$\implies \: {x}^{2} + 18x = 208$

$\implies \: {x}^{2} + 18x - 208 = 0$

$\implies \: {x}^{2} - 8x + 26x - 208 = 0$

$\implies \: x(x - 8) + 26(x - 8) = 0$

$\implies \: (x - 8)(x + 26) = 0$

$\implies(x - 8) = 0 \: \: or \: \: (x + 26) = 0$

$\implies \: x - 8 = 0 \: \: or \: \: x + 26 = 0$

$\implies \: x = 8 \: \: or \: \: x = - 26$

$\because \bold{ \: x \: cannot \: be \: negative.}$

$\therefore \: x = 8$

$\scriptsize\bold{\therefore \: Square \: of \: the \: larger \: number = 18x}$

$\bold{ = 18 \times 8}$

$\bold{ = 144}$

$\bold{So, the \: larger \: number \: is = \sqrt{144} }$

$\bold{ = 12}$

$\bold{Hence \: the \: number \: are \: 8 \: and \: 12}$