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This is an example of number problems. We have to translate the word problem into algebraic expressions.

Let x = the first number 16 - x = the second number

The sum of two the square of each number is 146 can be written as this

Let's solve for x

(x - 11)(x - 5) = 0 x - 11 = 0 x - 5 = 0 x = 11 x = 5

Since the algebraic expression "sum", means you add them and the answer is 16 x+y=16

The sum of their square is 146 means if you add their square, the answer is 146. x²+y²=146

You now have: x+y=16 x²+y²=146

First find the value of y in the first equation: x+y=16 y=16-x

Substitute to the second equation x²+(16-x)²=146 x²+256-32x+x²=146 Add like terms 2x²-32x+256=146 Divide both sides by 2 x²-16x+128=73 Subtract both sides by 73 x²-16x+55=0 Factor out: (x-11)(x-5)=0 x-11=0 x-5=0 x=11 x=5

Now find the two numbers: a)if x=11 x+y=16 11+y=16 y=5