It's a very common trick in these math puzzles, especially when you have X squared and X cubed, to use one of the three properties: the difference of squares, the sum of cubes and the difference of 😅 of cubes. using these formulas allows, you, usually, to factor out a binomial and a quadratic, which makes it, then, easy to solve.
In step 3 you instantly wrote -16 & -64. You didn’t explain how you arrived at those numbers. True, 16 plus 64 is 80, but so is 30 plus 50, and 10 plus 70 etc.
This is an experienced problem solver and he recognized 16 is the same as 4 squared and 64 = 4 cubed (4x4x4). The experienced fact comes into play at 2:25 in the video when he uses the identities. Hope this helps.
This guy knows by trial and error or using a formula for finding roots of third order Equations that x=-4 is a root, then he divides his third order polynomial by x+4 and he gets his second order Equations. After that he goes backwards and find out that 80=64+16 is the correct splitting and he makes his Nice video.
I feel sorry for your question as you will not get answer either they will tell you to check certain link till you give up like I did. I asked them if in the case of large number how do I get the sqs and cubes at the earliest and had no answer. With these the teacher already calculated and got those two figures before lecturing.
According to the fundamental theorem of algebra, since your highest exponent is three, you're going to have three roots. In this case, you have one real root and two complex roots.The equation factored out into one quadratic and one binomial multiplied together and =0, This means all or one of the factors is equal to 0, so when you set the binomial = 0 you get x= -4 and when you set the quadratic=0 you get x is equal to 2 complex roots.
My question: If the function on the left is an integer, does that mean that x must be an integer? I assumed so, and also saw it had to be a negative number (because x^3 was less than x^2). So I plugged in the smallest one that seemed about right, and yes, it was -4.
I figured x had to be a negative number so I just started at -2 and applied the equation then worked my way up. (or down). Yep, x=-4. It took Rashel nearly 10 minutes to solve, introducing values for a, b and c. Why! I’m starting to think that this is a joke.
X=-4 is a root of the equation. Then we divide the polynomial x^3-x^2+80 on x+4 and find 2 more roots.
1. x^2 - x^3>0 => unless 1 root x^3 - x^2 + 80=0 => (x+4) (x^2 -3x + 20) = 0 ，solve by standard form.
It's a very common trick in these math puzzles, especially when you have X squared and X cubed, to use one of the three properties: the difference of squares, the sum of cubes and the difference of 😅 of cubes. using these formulas allows, you, usually, to factor out a binomial and a quadratic, which makes it, then, easy to solve.
X= -4,x^2-x^3=x(x-x^2)=80 so part in brackets multiplied by x must equal 80,& since x must have the same value the only number that works is -4 2:34
In step 3 you instantly wrote -16 & -64. You didn’t explain how you arrived at those numbers. True, 16 plus 64 is 80, but so is 30 plus 50, and 10 plus 70 etc.
This is an experienced problem solver and he recognized 16 is the same as 4 squared and 64 = 4 cubed (4x4x4). The experienced fact comes into play at 2:25 in the video when he uses the identities. Hope this helps.
@@smokeon1633 Надо знать теорему Безу
This guy knows by trial and error or using a formula for finding roots of third order Equations that x=-4 is a root, then he divides his third order polynomial by x+4 and he gets his second order Equations. After that he goes backwards and find out that 80=64+16 is the correct splitting and he makes his Nice video.
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I feel sorry for your question as you will not get answer either they will tell you to check certain link till you give up like I did. I asked them if in the case of large number how do I get the sqs and cubes at the earliest and had no answer. With these the teacher already calculated and got those two figures before lecturing.
x^2(1--x)=4^2(5)etc
x^2-x^3=80
×^2(1-×)=80
2×(-2)×2×(-2)×5=80
(1-×)=5
×=-4
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x = -4 is the answer
(-4)² -(-4)³ = 16-(-64)= 16+64=80
yes ,thanks my friend ❤️
According to the fundamental theorem of algebra, since your highest exponent is three, you're going to have three roots. In this case, you have one real root and two complex roots.The equation factored out into one quadratic and one binomial multiplied together and =0, This means all or one of the factors is equal to 0, so when you set the binomial = 0 you get x= -4 and when you set the quadratic=0 you get x is equal to 2 complex roots.
4 is obvious-Mathlete 101.Synthetic division gives other roots.
Here we used substitution to find the answer
Solved in only 2 seconds
😮
My question: If the function on the left is an integer, does that mean that x must be an integer? I assumed so, and also saw it had to be a negative number (because x^3 was less than x^2). So I plugged in the smallest one that seemed about right, and yes, it was -4.
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x=2, 4-8=-4, -4y=80, y=-20
Nice maths problem❤
Thanks 🤗
ممتاز. GOOOOOD
Pls is there any way of coming out with 16 and 64.
-4
X=2, 4-8=-4, -4y=80, y=-20, then solve x
ok 😮
80=(-4)^2×5=x^2×(1-(-4))
Looking both side
X=-4
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You assume that the figure given is an easy to split into square and cube root complex. What if it isn't ? Your explanation lacks a spice of accuracy
Wow that looks very complicated i used mental math and got x=-4, do you need to show your work in the entrance exam?
I figured x had to be a negative number so I just started at -2 and applied the equation then worked my way up. (or down). Yep, x=-4. It took Rashel nearly 10 minutes to solve, introducing values for a, b and c.
Why!
I’m starting to think that this is a joke.
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Stop. You are wrong.
The questioner should mention that imaginary numbers need to be included.
its ok ❤
Easy Maths
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Compare to your explanation your writing is excellent, am i right guys
X=-4
thanks ❤
Tetap tidak paham 🗿
Х равен 4,даже к бабке не ходи😂.
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5 sn = - 4 😂 boşuna bu kadar işlem.
x= -4