Hello! And thank you for your question!
First we are going to redo the equation:
<span><span><span>y<span><span>^3</span><span></span></span></span>−3<span>y^<span><span>2</span><span></span></span></span>(3)+3(y)×<span>3<span><span>^2</span><span></span></span></span>−<span>3<span><span>^3</span><span></span></span></span>=0
Then we are going to use Cube of Difference:
0 = (y - 3)^3
That take cube root of both sides:
0 = y - 3
Finally add 3 to both sides:
3 = y
Final Answer:
y = 3</span></span>
Step-by-step explanation:
we have y intercept -10
and slope 3
we know the equation of line in slope -intercept form
y=mx+b
where m is slope and b is y-intercept
so the final equation would be
y=3x-10
Answer:
20
Step-by-step explanation:
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
