Question

The difference between squares of two numbers is 120. The square of smaller

number is twice the greater number. Find the numbers.​

Answer 1

Answer:

Numbers are 12 and 24.

Step-by-step explanation:

Let the no. be x and y.

${x}^{2} - {y}^{2} = 120 - - - - > 1 \\ {y} = 2 x - - - - > 2 \\ putting \: value \: of \: 2 \: in \: 1 \\ {x}^{2} - 2 {x} = 120 \\ {x}^{2} - 2x - 120 = 0 \\ {x}^{2} - (12 - 10)x - 120 = 0 \\ {x}^{2} - 12x + 10x - 120 = 0 \\ x(x - 12) + 10(x - 12) = 0 \\ (x - 12)(x + 10) \\ x - 12 = 0 \\ x = 12 \\ \\ x + 10 = 0 \\ x = - 10 \\ \\ since \: no. \: cannot \: be \: negative \\ so \: x = 12 \\ y = 2 \times 12 \\ y = 24$

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Answer 2

⠀ ☆.QUESTION.☆

The difference between squares of two numbers is 120. The square of smaller

number is twice the greater number. Find the numbers ?

⠀  ✪.ANSWER.✪ 

Let, two number are x and y .

A/C to Question

( The difference between squares of two numbers is 120 )

↪ ( x² - y² ) = 120 ..............[ Equ(1) ]

Again,

( The square of smaller number is twice the greater number )

↪( y² = 2x ) . ........... [ Equ(2) ]

Keep Value In equ (1)

↪( x² - 2x -120 ) = 0

↪( x² - 12x +10x - 120 ) = 0

↪ x(x-12) +10(x-12) = 0

↪ (x-12)(x+10) = 0

↪( x -12 ) = 0 or, ( x +10 ) = 0

↪ x = 12 or. x = -10

( Keep Value in equ. (2) .

When,

• x = 12,

↪ y² = 2 × 12

↪ y² = 24

↪ y = 2√6

When,

• x = -10

↪ y² = 2 × -10

↪ y ² = -20

↪ y = √(-20).

But, When x = -10, value of y is imaginary ,

So, x = -10 , and y = √(-20) is negligible ,

Then, We take

➡ Value of x = 12

➡ Value of y = 2√6

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ANSWER VERIFICATION

Case(1):-

( The difference between squares of two numbers is 120 )

↪ ( x² - y² ) = 120

↪{ 12² - (2√6)² } = 120

↪ ( 144 - 24 ) = 120

↪ 120 = 120

L.H.S. = R.S.H.

(First case is proved )

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Case(2) :-

( The square of smaller number is twice the greater number )

➡( y² = 2x )

➡ (2√6)² = 2 × 12

➡ 4 × 6 = 24

➡ 24 = 24

L.H.S.=R.H.S

(Second condition is proved )

Here , Both Condition are satisfy ,

So, We can say that Our solution are right .

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