Question

if x y z is equal to 9 and xy + Y Z plus ZX is equals to 23 then the value of x cube + y cube + Z cube minus 3 x y z is equal to ​

Answer 1

Step-by-step explanation:

Correct Question :-

If x + y + z = 9 and xy + yz + zx = 23 Then, find the value of x³ + y³ + z³ - 3xyz

Solution :-

Given -

• x + y + z = 9
• xy + yz + zx = 23

→ -1(-xy - yz - zx) = 23

→ -xy - yz - zx = -23

To Find -

• Value of x³ + y³ + z³ - 3xyz

As we know that :-

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

→ (9)² = x² + y² + z² + 2(xy + yz + zx)

→ 81 = x² + y² + z² + 2(23)

→ x² + y² + z² = 81 - 46

→ x² + y² + z² = 35

Now,

As we know that :-

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

→ (9)(35 - 23)

→ 9 × 12

→ 108

Hence,

The value of x³ + y³ + z³ - 3xyz is 108

Answer 2

Step-by-step explanation:

> (x3 + y3 + z3 - 3xyz)

= (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

= (x + y + z) [(x + y + z)2 - 3(xy + yz + zx)]

= 9 x (81 - 3 x 23)

= (9 x 12)

= 108