If x, y, z are real numbers such that x + y + z = 10 and xy + yz + zx = 18, then what is the value of x³ + y³ + z³ - 3xyz?
460
We know that x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx) x + y + z = 10 xy + yz + zx = 18 (x + y + z)² = x² + y² + z² + 2(xy + yz + zx) 10² = x² + y² + z² + 2(18) 100 = x² + y² + z² + 36 x² + y² + z² = 64 x³ + y³ + z³ - 3xyz = (10)(64 - 18) = 10(46) = 460
Important Questions from Algebra
The difference between the two positive numbers x and y where x > y, is 25% of x. If the value of y is 15, then the value of x is:
If p2 + q2 - r2 = 0, then the value of (p6 + q6 - r6) ÷ p2q2r2 is:
If √2 + √x = √3, then the value of x is equal to:
The sum of two numbers is 20 and their difference is 2.5. Ratio of these numbers will be:
If \(\rm \frac{\sqrt{19 - x \sqrt{12}}}{1} = \sqrt 4 - \sqrt 3\) then the value of x is equal to:
