find the value of xy+yz+zx if x+y+z =8,x^2+y^2+z^2pl
Answers
Answer:
If x+y+z=8 and xy+yz+zx=20, find the value of x
3
+y
3
+z
3
−3xyz
Study later
ANSWER
Given, x+y+z=8,xy+yz+zx=20
Now, x
3
+y
3
+z
3
−3xyz=(x+y+z)(x
2
+y
2
+z
2
−xy−yz−zx)
Again, (x+y+z)
2
=x
2
+y
2
+z
2
+2xy+2yz+2zx
x
2
+y
2
+z
2
=(x+y+z)
2
−2(xy+yz+zx)
x
2
+y
2
+z
2
=(8)
2
−2(20)=24
x
3
+y
3
+z
3
−3xyz=(x+y+z)[x
2
+y
2
+z
2
−(xy+yz+zx)]
x
3
+y
3
+z
3
−3xyz=(8)[24−(20)]
x
3
+y
3
+z
3
−3xyz=(8)[24−(20)]=8(4)=32
Step-by-step explanation: MARK ME AS BRAINLIEST
Step-by-step explanation:
if x+y+z =8 and xy + yz + zx = 20 , find the valuw of x
3
+y
3
+z
3
study later
given , x+y+z=8 , xy+yz+zx=20
now, x
3 +y
3 +z
3
-3xyz=(x+y+z) (x2 +y2 +z2 -xy-yz-zx)
again , (x+y+z)
2 = x2+y2+z2 +2xy+2yz+2zx
x
2
+y
2
+z
2
=(x+y+z) 2
-2(xy+yz+zx)
x2+y2+z2 =8
2-2(20) =24
x3+y3+z3- 3xyz=(x+y+z) [ x2+y2+z2 -(xy+yz+zx)]
x3+y3+z3 - 3xyz = (8)[24-(20)]
x3+y3+z3-3xyz =(8)[24-20)]=8(4)=32