Question

Find the value of x^3+ y^3 + z^3, if
x + y + z = 11, x^2 + y^2 + z^2 = 45 and xyz = 40​

Answer 1

Answer:

197

Step-by-step explanation:

put value of x= 5y= 2,z= 4

solve direct

x³+y³+z³= 125+64+8= 197 √√√

Answer 2

Answer :-

Value of x³ + y³ + z³ is 197.

Explanation :-

Finding the value if xy + yz + xz

We know that

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

Here

• x² + y² + z² = 45

• x + y + z = 11

By substituting the value in the identity

⇒ (11)² = 45 + 2(xy + yz + xz)

⇒ 121 = 45 + 2(xy + yz + xz)

⇒ 121 - 45 = 2(xy + yz + xz)

⇒ 76 = 2(xy + yz + xz)

⇒ 76/2 = xy + yz + xz

⇒ 38 = xy + yz + xz

⇒ xy + yz + xz = 38

Finding the value of x³ + y³ + z³

We know that

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

Here

• x + y + z = 11

• xyz = 40

• xy + yz + xz = 38

• x² + y² + z² = 45

By substituting the values in the identity

⇒ x³ + y³ + z³ - 3(40) = (11)(45 - 38)

⇒ x³ + y³ + z³ - 120 = 11(7)

⇒ x³ + y³ + z³ - 120 = 77

⇒ x³ + y³ + z³ = 77 + 120

⇒ x³ + y³ + z³ = 197

∴ the value of x³ + y³ + z³ is 197