Question
If 2x + 4y - 9 = 0, then find the value of 8x 3
- 723 + 64y 3 + 216xy.Solution
2x + 4y - 9 = 0
If, a + b - c = 0, then, a 3 + b 3 - c 3 = - 3abc
So, (2x) 3 + (4y) 3 + ( - 9) 3 = - 3 X (2x) X (4y) X (9)
Or, 8x 3 + 64y 3 - 729 = - 216xy
Or, 8x 3 + 64y 3 - 729 + 216xy = 0 ....(i)
8x 3 - 723 + 64y 3 + 216xy = 8x 3 - 729 + 6 + 64y 3 + 216xy
Put the value of equation (i) in the above equation, we get,
8x 3 - 723 + 64y 3 + 216xy = 0 + 6 = 6
The Newton-Raphson method is an iterative technique primarily used for:
Which type of data can be ordered, but the differences between values are not meaningful (e.g., satisfaction ratings: "Good," "Better," "Best")?
The "standard deviation" is the square root of which other statistical measure?
In numerical computing, what type of error occurs when a continuous function is approximated by a discrete sum or a finite number of terms?
Which numerical method approximates the definite integral of a function by dividing the area under the curve into trapezoids?
What does a p-value less than a significance level (e.g., 0.05) typically indicate in hypothesis testing?
Which statistical measure quantifies the average squared deviation of each data point from the mean?
Relevant for Exams:
