The value of - 45 x³ y³ z³ ÷ - 9 x² y² z² is
Answers
Answer:
x^2+y^2+z^2=38
Now,we have a formulae -(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
Putting known values in above formulae,we get
100=38+2(xy+yz+zx) or (xy+yz+zx)=62/2=31
Now,we are also given with x^3+y^3+z^3=160
We have a formulae -
x^3+y^3+z^3–3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
Putting known values in above equation,we get
160–3xyz=(10)(38–31) {Since,we have already got the value of xy+yz+zx}
160–3xyz=70 or 3xyz=90 or xyz=30
Thus,value of xyz=30
Hope this helps…
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Som Agrawal
Updated 2 years ago
I think it can be directly solved by objective approach…..
See how ….
Going through the question I think it would be lenthy to solve ( x+y+z)^2 and (x+y+z)^3 ,then substituting the value of x^2+y^2+z^2 and x+y+z….
Instead of that ….
Write x+y+z=10 as 5+2+3
x^2+y^2+z^2=38 as 25+4+9=5^2+2^2+3^2
And…
x^3+y^3+z^3=160 as 125+8+27=160
So the solution becomes …..
x=5,y=2 ,z=3 and vice versa….
So xyz=5*2*3=30
Abhimanyu Singh
Answered 4 years ago
We can easily relate (x+y+z) , (x2+y2+z2) , and (x3+y3+z3) :
(x+y+z)3−3(x+y+z)(x2+y2+z2)+2(x3+y3+z3)=6xyz
Now, plugging in the values, Simply solves this:
⇒6xyz=103−3×10×38+2×160=180
⇒xyz=30 .
If x3+y3+z3=305 and x2+y2+Z2=105, what is xy+yz+zx?
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Akshay Pal
Answered 4 years ago
X=2,Y=3,Z=5 satisfy to all three eqn
XYZ=30
First find the the value of xy+yz+zx.
By identity
(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xy …..1
x+y+z=10 ,x^2+y^2+z^2=38 both of put on eqn 1
We get xy+yz+zx=31
Now, with the help of
x^3+y^3+z^3–3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx) …2
now put all the known Value in eqn 2
We get xyz=30
Umesh Sharma
Lean Six Sigma Green Belt Certification by VarSigma.
Nachiket Agrawal
Answered 4 years ago
Ok i didn't solve it but it seems that (2,3,5) is the only solution
So xyz=30
PS:I had encountered this question before are that time it struck to me that (2,3,5) is supposedly the only solution
I may be wrong
Shubham Tiwari
Answered 4 years ago
Thanks…
Umesh Sharma
Joyce Vedasundaram
Updated 1 year ago
Dinesh Kewlani
Answered 4 years ago
X =2 y= 3 z = 5
Vàsudeva Rao Narsipuram
Answered 4 years ago
X=2, Y=3, Z=5
Mohana Priya
Answered 4 years ago
X=2 y=3 z=5
Sagar Patil
Answered 4 years ago
2,3,5
Answered 1 year ago
Girish Pawar
Answered 1 year ago
14
Virat Sharma
Answered 4 years ago
90
Kashish Mistry
Answered 4 years ago
30
Niraj Singh Rathore
Answered 4 years ago
30
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