A multiplication is zero if and only if at least one of the factors is zero. So, in this case, the multipications equals zero when
The first equation has no real solutions, because 
is a square, and thus it's positive. If you add 4 to a positive number, the result can't be zero.
The second equation has the solution
So, globally, the expression equals zero if and only if 
Step-by-step explanation:
4+9+8+6+5+44+88+90+78= 332
Step-by-step explanation:
Given functions are:
The operations on functions can be performed just as they are performed on polynomials
So
Combining like terms
Hence,
Keywords: Functions
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Equation 1) -x - y - z = -8
Equation 2) -4x + 4y + 5z = 7
Equation 3) 2x + 2z = 4
Solving for three variables is quite similar to solving for two variables. Just like when solving for two variables, you look for like variables & solve them one-by-one. So, let's get started! :)
Multiply ALL of equation 1 by four.
1) 4(-x - y - z = -8)
Simplify.
1) -4x - 4y - 4z = -32
Both equations 1 & 2 have the same three variables (x, y, z), so, we must look at these equations together.
1) -4x - 4y - 4z = -32
2) -4x + 4y + 5z = 7
Add these equations together, and create a fourth equation.
4) -8x - z = -25
Now, notice how both equations 3 & 4 have the same two variables (x, z).
So, we must look at these equations together.
3) 2x + 2z = 4
4) -8x - z = -25
Multiply ALL of equation 4 by 2.
4) 2(-8x - z = -25)
Simplify.
4) -16x - 2z =-50
3) 2x + 2z = 4
Now, add the equations together, so that we can solve for x.
-14x = -42
Divide both sides by -14.
x = 3
Now, plug in 3 for x into our 3rd equation.
3) 2x + 2z = 4
3) 2(3) + 2z = 4
Simplify.
6 + 2z = 4
Subtract 6 from both sides.
2z = 4 - 6
Simplify.
2z = -2
Divide both sides by 2.
z = -1
Now, plug in -1 for z & 3 for x in our 1st equation.
1) -x - y - z = -8
-(3) - y - (-1) = -8
Simplify.
-3 - y + 1 = -8
Simplify.
-2 - y = -8
Add 2 to both sides.
-y = -8 + 2
Simplify.
-y = -6
Divide both sides by -1.
y = 6
SO :
x = 3, y = 6, z = -1
~Hope I helped!~
