Question

If x + y + z = 5, xy + yz + zx = 8 and (x + y) (y + z)(z + x) = 36, then xyz is equal to what

Answer 1

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.

Answer 2

Step-by-step explanation:

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