Advertisements
Advertisements
Question
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Advertisements
Solution
(x + y + z)2 = (12)2
⇒ x2 + y2 + z2 + 2xy + 2yz + 2zx = 144
⇒ x2 + y2 + z2 + 2(xy + yz + zx) = 144
⇒ x2 + y2 + z2 + 2(27) = 144
⇒ x2 + y2 + z2
= 144 - 54
= 90.
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
95 × 96
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Evaluate of the following:
463+343
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
Evaluate: (4 − ab) (8 + ab)
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
