Question

✯ Question :-
If the sum of two positive square are 765. Also, the first square is greater than other by 3. Then find the number​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• The sum of the 2 positive square is 765. The square of the 1st number is greater than the other number by 3.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• The numbers

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• The sum of the 2 positive square numbers is 765.

First,

• Let the 1st number be x and 2nd number be y.

According to the question,

• x² + y² = 765

Second,

• The square of 1st number is greater than the other by 3.

This implies that,

• x = y + 3

• x² = (y + 3)²

• x² = y² + 9 + 6y

Substituting x² = y² + 9 + 6y in x² + y² = 765,

• x² + y² = 765

• y² + 9 + 6y + y² = 765

• 2y² + 6y + 9 = 765

• 2y² + 6y = 765 - 9

• 2y² + 6y = 756

• 2y² + 6y - 756 = 0

• 2 (y² + 3y - 378) = 0

• y² + 3y - 378 = 0

Using PSF method,

• P = - 378 * y² = - 378y²

• S = + 3y

• F = + 21 y , - 18 y

Now,

• y² + 21y - 18y - 378 = 0

• y (y + 21) - 18 (y + 21) = 0

• (y + 21) (y - 18) = 0

• y + 21 = 0 , y - 18 = 0

• y = - 21 , y = + 18

Since, numbers cannot be negative.

• y = 18

Now,

• x = y + 3

• x = 18 + 3

• x = 21

Therefore,

• $\underline{\boxed{\purple{\tt{The \: two \: numbers \: are \: 21 \: and \: 18.}}}}$

$\Large{\bf{\blue{\mathfrak{\dag{\underline{\underline{Verification:-}}}}}}}$

• x² + y² = 765

• 21² + 18² = 765

• 441 + 324 = 765

• 765 = 765

LHS = RHS

Hence, verified.

Answer 2

Question :

If the sum of two positive square are 765. Also, the first square is greater than other by 3. Then find the number

Solution :

Let the numbers be x and y.

Now x + y = 765 …(1)

x - y = 3 …(2). Add (1) and (2) to get

2x = 768, or

x = 384, so y = 765 - 384 = 381.

The difference of the their squares is (384+381)(384-381) = 765 × 3 = 2,295.

Check: The difference of their squares

= 384^2 - 381^2 = 147,456 - 145,161

= 2,295

The difference of the squares of the two numbers is = 765.

Answer :

The difference of the squares of the two numbers is = 765.