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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

Therefore, the two numbers are 11 & 5.

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

Therefore, the two numbers are 11 & 5.

x=first number

y=second number

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

b)if x=5

x+y=16

5+y=16

y=11

Hope this helps =)