Question

The difference of the squares of two natural numbers is 84. The square of the

larger number is 25 times the smaller number. Find the numbers​

Answer 1

Answer:

your answer is hear

Step-by-step explanation:

Answer

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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.

---A

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

---B

Substitute the value of in A

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

At y = 21

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

At y = 4

Thus the two natural numbers are 100 and 4.

Answer 2

Answer:

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.

Rightarrow x^2-y^2=84⇒x

2

−y

2

=84 ---A

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

x^2=25yx

2

=25y ---B

Substitute the value of x^2x

2

in A

Rightarrow 25y-y^2=84⇒25y−y

2

=84

Rightarrow y^2-25y+84=0⇒y

2

−25y+84=0

Rightarrow y^2-21y-4y+84=0⇒y

2

−21y−4y+84=0

Rightarrow y(y-21)-4(y-21)=0⇒y(y−21)−4(y−21)=0

Rightarrow (y-21)(y-4)=0⇒(y−21)(y−4)=0

Rightarrowy=21,4

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

x^2=25y

At y = 21

x^2=25(21)

x^2=525

x=\sqrt{525}

x=\sqrt{525}

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

At y = 4

x^2=25(4)

x^2=100

x=\sqrt{100}

x=10

Thus the two natural numbers are 100 and 4.