InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If the values of x, y and z are 256, -113 and -135, then find the value of the expression \(\frac{{{x^{3\;}}\; + \;{y^3}\; + \;{z^3} - \;3xyz\;}}{{{{\left( {x - y} \right)}^2}\; + \;{{\left( {y - z} \right)}^2}\; + \;{{\left( {z - x} \right)}^2}}}\)?1. 102. 43. 64. 8 |
|
Answer» Correct Answer - Option 2 : 4 Given: X = 256 Y = -113 Z = -135 Formula used: ⇒ x3 + y3 + z3 – 3xyz = (1/2) × (x + y + z)[(x – y)2 + (y – z)2 + (z – x)2] Calculation: ∵ x3 + y3 + z3 – 3xyz = (1/2) × (x + y + z)[(x – y)2 + (y – z)2 + (z – x)2] ⇒ (x3 + y3 + z3 – 3xyz)/[(x – y)2 + (y – z)2 + (z – x)2] = (1/2) × (x + y + z) ⇒ (x3 + y3 + z3 – 3xyz)/[(x – y)2 + (y – z)2 + (z – x)2] = (1/2) × (256 – 113 – 135) = (1/2) × (256 – 248) = (1/2) × 8 = 4 |
|