if x+y+z=6, x2+y2+z2=14, x3+y3+z3=36 find the value of xyz
Answers
Answered by
2
X+Y+Z=6
X²+Y²+Z²=14
X³+Y³+Z³=36
WE HAVE (X+Y+Z)³=X³+Y³+Z³+3(X+Y)(Y+Z)(X+Z)
6³=36+(3X+3Y)(XY+ZY+ZX+Z²)
216-36=3(X²Y+XYZ+ZX²+XZ²+Y²X+ZY²+XYZ+YZ²)
180/3=2XYZ+X²Y+ZX²+XZ²+Y²Z+ZY²+YZ²)
SIMPLYFYING THIS U WILL GET A EQUATION.
SOLVE THIS EQUATION USING GIVEN APPROPRIATE EQUATION.
Answered by
2
Answer:
Step-by-step explanation:
X+Y+Z=6
X²+Y²+Z²=14
X³+Y³+Z³=36
WE HAVE (X+Y+Z)³=X³+Y³+Z³+3(X+Y)(Y+Z)(X+Z)
6³=36+(3X+3Y)(XY+ZY+ZX+Z²)
216-36=3(X²Y+XYZ+ZX²+XZ²+Y²X+ZY²+XYZ+YZ²)
180/3=2XYZ+X²Y+ZX²+XZ²+Y²Z+ZY²+YZ²)
SIMPLYFYING THIS U WILL GET A EQUATION.
SOLVE THIS EQUATION USING GIVEN APPROPRIATE EQUATION
Similar questions