These are the three questions that I'm struggling with. Question 2 is a matter of terminology. Questions 1 and 3 are just difficult for me to decipher through and are causing me some confusion. (The initial set of directions apply to each question).
1. Assign a value to the variable "x" to make the equation a true statement.
(x^2 + 5)(3 + x^4)(100x^2 - 10)(100x^2 + 10) = 0
2. The diagonal of a square of side length L is 2 inches long when ____.
3. √x + √5 = √x + 5
Thank you!
#1 is an example of why we always set factored expressions to zero. If the product of several factors is zero, one of the factors must be zero. So, we must have one of the following:
x^2+5 = 0 Cannot happen
x^4+3 = 0 Cannot happen
100x^2-10 = 0: x = ±1/√10
100x^2+10 = 0 Cannot happen
#2 The diagonal of a square of side L is L√2, so
L√2 = 2
L = √2
#3 There are no solutions. If you subtract √x from both sides, you get
√5 = 5
Now, if you were just careless with parentheses, and meant
√x + √5 = √(x+5)
then start by squaring both sides:
x+2√(5x)+5 = x+5
2√(5x) = 0
x=0