If the difference of two numbers is 8

Asked by admin @ 29/08/2021 in Math viewed by 371 People

If the difference of two number is 8 and the difference of their squares is 160 then the numbers are

Answered by admin @ 29/08/2021

Answer:

The two numbers are 6 and 14

Step-by-step-explanation:

Let the two numbers be x and y

Given,

x - y = 8...... i)

x² - y² = 160.......ii)

From equation i), we get

x = y + 8

Now, by putting this value in equation ii)

(y + 8)² - y² = 160

☛ y² + 16y + 64 - y² = 160

y² and -y² gets cancelled as their sum will be zero

☛ 16y + 64 = 160

☛ 16y = 160 - 64

☛ 16y = 96

☛ y = 6

Now, putting the value of y as 6

x - y = 8

☛ x - 6 = 8

☛ x = 8 + 6

☛ x = 14

∴ $\textbf{The two numbers are 6 and 14}$

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