Question

The sum of squares of two numbers is 80 and the square of difference between the two numbers is 36. Find the product of two numbers. *

Answer 1

Answer:

First condition: [math]a^2+b^2=80[/math]

Second condition: [math](a-b)^2=36[/math]

From second condition: [math]a^2-2ab+b^2=36[/math].

Replacing first condition: [math]80-2ab=36[/math], reorganizing [math]2ab=80-36=44[/math]

So [math]2ab=44[/math] and [math]ab=22[/math].

The answer: the product is 22.

Answer 2

Answer:

The answer is 22.

Let the two numbers be x, and y.

The conditions given are:

The sum of squares of two numbers is 80.

x²+y²=80

The square of difference between the two numbers is 36.

(x-y)²=36

x²-2xy+y²=36

Take the second condition, and derive a value for x².

x²-2xy+2xy+y²-y²=36+2xy-y²

x²=-y²+2xy+36

Replace x² in the first condition with the derived value.

x²+y²=80

(-y²+2xy+36)+y²=80

y²-y²+2xy+36=80

2xy+36–36=80–36

2xy÷2=44÷2

xy=22

Thus the product of the two numbers (x,y) is 22.