I just answered this xD
1-3 is given as an example.
4. True
5. False. It is the same thing twice
6. True
Answer:
x² -3/4x +1/4 = 0
Step-by-step explanation:
Consider the two equations in factored and expanded forms:
(x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0 ⇒ p²+q² = 1, p²q² = 16
and
(x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0
Consider the squares of the sum and product of roots:
constant term: (1/(pq))² = 1/(p²q²) = 1/16 ⇒ 1/(pq) = √(1/16) = 1/4
x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)
= (p² +q²)/(p²q²) +2/(pq)
= 1/16 +2/√16 = 9/16 ⇒ (1/p +1/q) = √(9/16) = 3/4
Then the equation with roots 1/p and 1/q is ...
x² -3/4x +1/4 = 0
Hello from MrBillDoesMath!
Answer: 21 ^ (1/3)
Discussion:
The cube root of a number is the same as raising the number of the third power.
Thank you,
MrB
120+25x=45x
Step 1: Simplify both sides of the equation.
25x+120=45x
Step 2: Subtract 45x from both sides.
25x+120−45x=45x−45x
−20x+120=0
Step 3: Subtract 120 from both sides.
−20x+120−120=0−120
−20x=−120
Step 4: Divide both sides by -20.
−20x
−20
=
−120
−20
x=6
Answer:
x=6
The answers are:
1. 6
2. I would go for 9 but I'm not for sure
i hope this helped
