Question

The sum of the numbers is 8 and the difference of their squares is 32. Find the numbers.​

Answer 1

Question

The sum of the numbers is 8 and the difference of their squares is 32. Find the numbers. .

Solution

Given:-

• The sum of the numbers is 8
• difference of their squares is 32

Find:-

• These two number .

Explanation

Let,

• first number = x
• Second number = y

A/C to question

(The sum of the numbers is 8)

==> x + y = 8 ------------equ(1)

Again,

(difference of their squares is 32 )

==> x² - y² = 32

We know,

★ (x²-y²) = (x+y)(x-y)

So,

==> (x+y)(x-y) = 32

keep value by equ(1)

==> x - y = 32/8

==> x - y = 4 ----------------equ(2)

Now, Add equ(1) & equ(2).

==> 2x = 12

==> x = 12/2

==> x = 6

keep value of x in equ(2),

==> 6 - y = 4

==> y = 6 - 4

==> y = 2

Hence

• Value of first number = x = 6
• Value of second number = y = 2

___________________

Answer 2

ANSWER :–

Numbers are 6 and 2.

EXPLANATION :–

GIVEN :–

• Sum of numbers is 8.

• Difference of their squares is 32.

TO FIND :–

Both Number.

SOLUTION :–

• Let the number is x and y.

➨ Sum of numbers = 8

=> x + y = 8 ——————eq.(1)

➨ Difference of their squares = 32

=> x² - y² = 32 ——————eq.(2)

• We know that –

➨ a² - b² = (a + b)(a - b)

• By equation (2) –

➨ (x + y)(x - y) = 32

➨ (8) (x - y) = 32 [ using eq.(1) ]

➨ (x - y) = 4 ––—–———–eq(3)

• Now add equation (1) and (3) –

➨ (x + y)+(x - y) = 8 + 4

➨ 2 x = 12

➨ x = 6

• Now put the value of 'x' in equation (1) –

➨ 6 + y = 8

➨ y = 2

VERIFICATION :–

(1) sum of numbers = 8

=> 2 + 6 = 8

=> 8 = 8 (verified)

(2) Difference of their squares = 32

=> (6)² - (2)² = 32

=> 36 - 4 = 32

=> 32 = 32 (verified)