The sum of the square of 2 numbers is 80 and the square of the difference between the numbers is 36. Find the product of the 2 numbers. Show your working.
a. 11
b. 22
c. 33
d. 26
Answers
Answered by
3
Answer:
22
Step-by-step explanation:
Let the two numbers be x and y.
(i) Sum of squares is 80.
⇒ x² + y² = 80
(ii) Difference between the numbers is 36.
⇒ (x - y)² = 36
⇒ x² + y² - 2xy = 36
⇒ 80 - 2xy = 36
⇒ -2xy = -44
⇒ xy = 22.
Therefore, Product of the two numbers is 22.
Hope it helps!
Answered by
3
The Sum of the square of two numbers is 80"
x^2 + y^2 = 80
"and the square of their difference is 36."
(x - y)^2 = 36
Foil (x-y)(x-y)
x^2 - 2xy + y^2 = 36
Use elimination, subtract from the 1st equation
x^2 + 0xy + y^2 = 80
x^2 - 2xy + y^2 = 36
------------------------Subtraction eliminates, both x^2 and y^2
2xy = 44
Divide both sides by 2
xy = 22
:
The product of two numbers is: 22
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