The difference of two numbers is 3 and the difference of their square is 69 . Find the numbers
Answers
Answered by
10
x = first number
y = second number
x - y = 3
x² - y² = 69
x = y + 3
(y + 3)² - y² = 69
y² + 6y + 9 - y² = 69
6y = 60
y = 10
x = y + 3 = 10 + 3 = 13
Checking:
x - y = 13 - 10 = 3
x² - y² = 13² - 10² = 169 - 100 = 69
y = second number
x - y = 3
x² - y² = 69
x = y + 3
(y + 3)² - y² = 69
y² + 6y + 9 - y² = 69
6y = 60
y = 10
x = y + 3 = 10 + 3 = 13
Checking:
x - y = 13 - 10 = 3
x² - y² = 13² - 10² = 169 - 100 = 69
Answered by
1
Step-by-step explanation:
Let the Two Numbers be A and B
Given : The Difference of Two Numbers is 3
⇒ A - B = 3
⇒ A = B + 3
Given : The Difference of their Squares is 69
⇒ A² - B² = 69
Substituting A = (B + 3) in the Above Equation, We get :
⇒ (B + 3)² - B² = 69
⇒ B² + 9 + 6B - B² = 69
⇒ 6B = 69 - 9
⇒ 6B = 60
⇒ B = 10
Substituting B = 10 in A = (B + 3), We get :
⇒ A = (10 + 3) = 13
So, The Two Numbers are 10 and 13
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