Question

two positive numbers are in the ratio 2:5 if the difference between the squares of these numbers is 189 find the numbers​

Answer 1

given ratio between two positive no.s = 2 : 5

let the two positive no.s be 2x and 5x.

ATQ, the difference between the squares of these no.s is 189

∴ (5x)^2 - (2x)^2 = 189

⇒ 25x^2 - 4x^2 = 189

⇒ 21x^2 = 189

⇒ x^2 = 189/21

⇒ x^2 = 9

⇒ x = √9 = 3

hence, the no.s are :-  

• 2x = 2 * 3 = 6

• 5x = 5 * 3 = 15

verification :-

= (15)^2 - (6)^2

= 225 - 36

= 189

HENCE VERIFIED.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

The numbers are 6 and 15.

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given that :

The ratio between two positive numbers is 2:5.

The difference between the squares of these numbers is 189.

To Find :

The two positive numbers.

Solution :

Let the two positive numbers be 3x and 2y.

So,

$\sf =>(2y)^2 - (3x)^2 = 189$

$\sf =>25y^2 - 4x^2 = 189$

$\sf=>21x^2 = 189$

$=> x^2 = \dfrac{189}{21}$

$\sf => x^2 = 9$

$x = \sqrt9 = 3$

So,

$2y = 2\times 3 = 6\\3x = 5 \times 3 = 15$

Hence,

The numbers are 6 and 15.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\sf=> (15)^2 - (6)^2\\\ => 225 - 36\\\ => 189$

Hence,

Our answer is correct.