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| General Mathematics |
Hey Guys, hope you are well.
Today we are going to Prove a math question (l.h.s=R.h.s) value in this article.
As you see in title,this equation is if x+y+z=0 show that x³+y³+z³=3xyz.
So if you love mathematics then you should read this article. To learn Algebra you should bookmark our site or you also follow us at SaRaisay.
In Many education board this math is given in the book of 9th standard or 10th standard.
As you know that this question is from algebra side.
So there are many ways to solve it.
Actually here main focus is how to make l.h.s=R.h.s .
So guys let's crack this question,stay with me and read this article carefully.
Bythe way if you want read article in hindi language then visit our hindi Blog.
So, let's start.
Solving: if x+y+z=0 show that x³+y³+z³=3xyz.
Basically ,to prove this equation there is two method.This methods are very easy to do.
I solve this math below from this methods.
Method 1
We know that
x³ + y³ + z³ - 3xyz
= (x + y + z)(x² + y² + z² - xy - yz - zx)
Now putting the value of x+y+z
Or,x³ + y³ + z³ - 3xyz = (0)(x² + y² + z² - xy - yz - zx) ( As x + y + z = 0)
Or,x³ + y³ + z³ - 3xyz=0
Or, x³ + y³ + z³ = 3xyz
Hence, L.H.S=R.H.S (proved)
Method 2
Given that x+y+z=0
Or, x+z=−y
Or,y³=-(x+z)³
Now consider the L.H.S part first
x³+y³+z³
=x³−(x+z)³+z³ (putting the value of y³)
=x³-(x³+3x²z+3xz²+z³)+z³ [(formula of (a+b)³]
=x³-x³-3x²z-3xz²-z³+z³ (bracket opened and all
sign change due to - sign)
=-3x²z-3xz²
=−3xz(x+z)
=3xyz (putting the value of x+z)
=R.H.S
Or, x³ + y³ + z³ = 3xyz
Hence, L.H.S=R.H.S (proved)
So,Those are the methods for solving this kind of Maths.
Conclusion
I know,This is not a easy math for all.
For that i discussed and solve this math through two method.
I hope it will help you lot.I think,you learn something today from this article.
I just want to say,do hard practice.
Because we all know that Practice is way to achieve something.
And in case of mathematics,it is well suited.
So,Do practice more and more.
Jai Hind