if y² + 1/y²=10 then, find the values of (y+1/y) (y-1/y) and hence verify 2( y²+1/y²)=(y+1/y)²+ (y-1/y)
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Answer:
Given x+y+z=12
Squaring it we get
x
2
+y
2
+z
2
+2(xy+yz+zx)=144
Therefore xy+yz+zx=24
Also 1/x+1/y+1/z=36
Implies (xy+yz+zx)/xyz=36
⇒xyz=(xy+yz+zx)/36=24/36=2/3
We know (x
3
+y
3
+z
3
)=(x+y+z)(x
2
+y
2
+z
2
−xy−yz−zx)+3xyz
⇒x
3
+y
3
+z
3
=(12)(96−24)+2=12∗72+2=866
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