If x + y + z = 5, xy + yz + zx = 8 and (x + y) (y + z)(z + x) = 36, then xyz is equal to what
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Answered by
25
Answer:
4
Step-by-step explanation:
Given :
- x + y + z = 5
- xy + yz + xz = 8
- ( x + y )( y + z )( z + x ) = 36
From the third equation
( x + y )( y + z )( z + x ) = 36
It can be written as
⇒ ( x + y + z - z )( x + y + z - x )( x + y + z - y )= 36
Substituting x + y + z = 5 in the equation we get,
⇒ ( 5 - z )( 5 - x )( 5 - y ) = 36
Since ( p - a )( p - b )( p - c ) = p³ - p²( a + b + c ) + p( ab + bc + ca ) - abc
⇒ 5³ - 5²( x + y + z ) + 5( xy + yz + zx ) - xyz = 36
Substituting x + y + z = 5 and xy + yz+ xz = 8 in the equation we get,
⇒ 5³ - 5²( 5 ) + 5( 8 ) - xyz = 36
⇒ 5³ - 5³ + 40 - xyz = 36
⇒ 40 - xyz = 36
⇒ 40 - 36 = xyz
⇒ 4 = xyz
⇒ xyz = 4
Therefore the value of xyz is 4.
RvChaudharY50:
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Answered by
8
Step-by-step explanation:
here's the soln....... you can check my YouTube channel... Lord Tedon
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