What is the sum of the squares of two numbers, the sum of which is 14 and their product is 8?  

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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...

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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

=> 180

Therefore the sum of the squares of the two numbers is 180.

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