If x+y+z=10 and xy+yz+zx=40 ,evaluate x2+y2+z2
Answers
Answered by
0
Answer:
I think 20 is the answer
Step-by-step explanation:
please mark as brainlest I need it
Answered by
1
Answer:
x+y+z=10 and x
2
+y
2
+z
2
=40.
Consider the square of (x+y+z)
2
as shown below:
(x+y+z)
2
=x
2
+y
2
+z
2
+2xy+2yz+2zx(∵(a+b+c)
2
=a
2
+b
2
+c
2
+2ab+2bc+2ca)
⇒(10)
2
=40+2(xy+yz+zx)(Givenx+y+z=10,x
2
+y
2
+z
2
=40)
⇒100=40+2(xy+yz+zx)
⇒100−40=2(xy+yz+zx)
⇒2(xy+yz+zx)=60
⇒xy+yz+zx=
2
60
⇒xy+yz+zx=30
Hence, xy+yz+zx=
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