What is the sum of the squares of two numbers, the sum of which is 14 and their product is 8?
Let the numbers to be determined be A and B.
Now the sum of the numbers is 14
=> A + B = 14.
The product of the numbers is 8
=> AB = 8.
We need to find the sum of the product of these numbers, for this we use the formula
(a + b)^2 = a^2 + b^2 + 2ab
=> a^2 + b^2 = (a + b)^2 - 2ab
A^2 + B^2 = (A+B)^2 – 2AB
=> 14^2 – 2*8
=> 196 – 16
Therefore the sum of the squares of the two numbers is 180.
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