Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
This is not middle school work
Answer:
all answers below
Step-by-step explanation:
(i) 2704 = 2^4 x 13^2
(ii) as both indices (the powers) are divisible by 2, it is a perfect square.
(iii) as both indices are not divisible by 3, it is not a perfect square.
Okay first you need to combine like terms together (3x and 1x)
7x + 4 = 5 + 4x
now you need x only on one side, you could subtract either 7x or 4x
3x + 4 = 5
subtract 4 over
3x = 1 is the answer
