Question

Find the value of x³ + y³ + z³ – 3xyz if x² + y² + z² = 83 and x + y + z = 15​

Answer 1

Step-by-step explanation:

ANSWER

Squaring both sides

(x+y+z)

2

=x

2

+y

2

+z

2

+2(xy+yz+zx)

we can substitute given values

(x+y+z)

2

=18+(2×9)

(x+y+z)

2

=36

(x+y+z)

Answer 2

Answer:

x2 + y2 + z2 = 83

and x + y+ z= 15

to find the value of x3+y3+z3-3xyz

solution;-

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

and

x+y+z= 15

so , 83+2(xy+yz+zx) = (15)2

or, 2 ( xy+ yz+zx) = 225-83

2(xy+yz+zx) = 142

(xy+yz+zx)= 142/2 = 71

again ;-

x2+y2+z2-3xyz= ( x+Y+z) [(x2+y2+z2) - (xy+yz+zx)]

or , 15 *[83-71]

then , 15*12

= 180

so the required value will be 180 .

Step-by-step explanation: hope this will help u dear . need feedback plz

itz akansha .