Question

The difference of the natural number is 7and their product is 450. find the number ​

Answer 1

Answer

Step-by-step explanation:

let x,y be required numbers

x-y=7

xy=450

x=7+y

(7+y)y=450

y²+7y-450=0 (solve equation by factorisation)

y=18,-25

if Y=18, from eqn1 ,x-18=7

x=25

if y = -25 then x= -18

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Answer 2

Answer:-

Let the numbers be a and b.

Given:

Difference of the numbers = 7

→ a - b = 7 -- equation (1)

And,

Product of the numbers = 450

→ ab = 450 -- equation (2)

We know that,

(a + b)² = (a - b)² + 4ab

→ (a + b)² = (7)² + 4 * 450

→ (a + b)² = 49 + 1800

→ (a + b)² = 1849

→ (a + b)² = (43)²

→ a + b = 43 -- equation (3)

Add equations (1) & (3).

→ a - b + a + b = 7 + 43

→ 2a = 50

→ a = 50/2

→ a = 25

Substitute a = 25 in equation (1)

→ a - b = 7

→ 25 - b = 7

→ 25 - 7 = b

→ 18 = b

Therefore, the required numbers are 25 , 18.