Question

$\sqrt{48}$
​

Answer 1

Answer:

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:-}}}}}}}†

ToFind:−

The numbers

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

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.}}}}

Thetwonumbersare21and18.

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

Verification:−

x² + y² = 765

21² + 18² = 765

441 + 324 = 765

765 = 765

LHS = RHS

Hence, verified.

Answer 2

$\huge \pink{ \boxed{ \sf{ \red{Question:-}}}}$

$➭ \sqrt{48}$

$\pink{ \boxed{ \sf{ \green{Answer:-}}}}$

⚽️ According to question:-

$= \sqrt{48}$

$= \sqrt{4 \times 4 \times 3}$

$= \sqrt[4]{3}$

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