Verify that x 3 + y 3 + z 3 – 3xyz = $\frac{1}{2}$ (x + y + z) [(x - y) 2 + (y - z) 2 + (z - x) 2 ].

Question

Verify that x 3 + y 3 + z 3 – 3xyz =  $\frac{1}{2}$  (x + y + z) [(x - y) 2 + (y - z) 2 + (z - x) 2 ].

cdquestions Admin · Accepted Answer

It is known that,  x 3 + y 3 + z 3 - 3xyz  = (x + y + z) (x 2 + y 2 + z 2 - xy - yz - zx)  =  $\frac{1}{2}$  (x + y + z) [2x 2 + 2y 2 + 2z 2 - 2xy - 2yz - 2zx]  = $\frac{1}{2}$  (x + y + z) [(x 2 + y 2 - 2xy) + (y 2 + z 2 - 2yz) + (x 2 + z 2 -2zx)]  =  $\frac{1}{2}$  (x + y + z) [(x - y) 2 + (y - z) 2 + (z - x) 2 ]

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Verify that x³ + y³ + z³ – 3xyz = \(\frac{1}{2}\) (x + y + z) [(x - y)² + (y - z)² + (z - x)²].

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions

Verify that x 3 + y 3 + z 3 – 3xyz = \(\frac{1}{2}\) (x + y + z) [(x - y)2 + (y - z)2 + (z - x)2].

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions

Verify that x³ + y³ + z³ – 3xyz = \(\frac{1}{2}\) (x + y + z) [(x - y)² + (y - z)² + (z - x)²].