Sagot :
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
[tex] x^{2} + (16-x)^{2} = 146[/tex]
Let's solve for x
[tex] x^{2} + 256 - 32x + x^{2} = 146[/tex]
[tex]2 x^{2} - 32x + 110 = 0[/tex]
[tex]( \frac{1}{2})(2 x^{2} - 32x + 110 = 0) [/tex]
[tex] x^{2} - 16x + 55 = 0[/tex]
(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
[tex] x^{2} + (16-x)^{2} = 146[/tex]
Let's solve for x
[tex] x^{2} + 256 - 32x + x^{2} = 146[/tex]
[tex]2 x^{2} - 32x + 110 = 0[/tex]
[tex]( \frac{1}{2})(2 x^{2} - 32x + 110 = 0) [/tex]
[tex] x^{2} - 16x + 55 = 0[/tex]
(x - 11)(x - 5) = 0
x - 11 = 0 x - 5 = 0
x = 11 x = 5
Therefore, the two numbers are 11 & 5.
Lets represent:
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 =)
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 =)