Question

the difference of squares of two natural numbers is 84 square of the largest number is 25 times the smallest number find the number​

Answer 1

Answer:

100 and 4.

Step-by-step explanation:

Let the two natural numbers be x and y

No we are given tha tThe difference of the squares of two natural numbers is 84.

x²- y² =84 ---A

We are also given that the square of the larger number is 25 times the smaller number

x²=25y ---B

Substitute the value of x² in A

$25y - y^{2} = 84 \\ {y}^{2} - 25y + 84 = 0 \\ {y}{2} - 21y - 4y + 84 = 0 \\ y(y - 21) -4(y - 21) = 0 \\ (y - 21)(y - 4) = 0 \\ 21 \: 4$

Substitute the values of y in B to get values of x

x²=25y

At y = 21

x²=25(21)

x²=525

x=√525

Since x is not natural number .So, we will reject this value

At y = 4

x²=25(4)

x²=100

x=√100

x=10

Thus the two natural numbers are 100 and 4.

hope this will help you:)

Answer 2

Answer:

100 and 4.

Step-by-step explanation:

Let the two natural numbers be x and y

No we are given tha tThe difference of the squares of two natural numbers is 84.

x²- y² =84 ---A

We are also given that the square of the larger number is 25 times the smaller number

x²=25y ---B

Substitute the value of x² in A

Thus the two natural numbers are 100 and 4.

y

2

−25y+84=0

y2−21y−4y+84=0

y(y−21)−4(y−21)=0

(y−21)(y−4)=0

214

=84Substitute the values of y in B to get values of x

x²=25y

At y = 21

x²=25(21)

x²=525

x=√525

Since x is not natural number .So, we will reject this value

At y = 4

x²=25(4)

x²=100

x=√100

x=10