Question

if the difference of two number is 3 and difference of their square is 39find the large number​

Answer 1

Answer : 8

Step by step explanation:

Let x be the larger number and y be the smaller.

Thus, As per your question,

x - y = 3.. (1)

x² - y² = 39.. (2)

From (1),

y = x - 3

Putting the value of y in (2),

So,

» x² - (x - 3)² = 39

» x² - x² + 6x - 9 = 39

» 6x = 48

» x = 8

Thus,

x = Larger number = 8

.°. The larger number is 8.

Answer 2

Answer:

Let the numbers be = x, y

Difference is 3 :

$\tt{x - y = 3}$ ...(1)

Difference of their squares is 39:

$\tt{x^{2} - y^{2} = 39}$

Open the squares by the identity :

$\tt{a^{2} - b^{2} = (a-b)(a+b)}$

=》 $\tt{(x-y)(x+y) = 39}$

Put (1) in this equation :

=》 $\tt{3(x+y) = 39}$

$\tt{x + y = 13}$ ...(2)

(1) - (2)

=》 $\tt{x = 8}$