If x + y + z = 0 then x3 + y3 + z3 + 3xyz is equal to ______.
6 xyz
Identity: x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx).
When x + y + z = 0, the right side is 0, so x3 + y3 + z3 = 3xyz.
x3 + y3 + z3 + 3xyz = 3xyz + 3xyz = 6xyz
Check: x = 1, y = 1, z = -2 gives 1 + 1 - 8 + 3(-2) = -12, and 6xyz = 6(-2) = -12.
Hence, 6 xyz.
Important Questions from Simplification
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done?
