Question
If, 3x + 2y = 15, and 2xy = 12, and 3x > 2y, then find
the value of 27x³ – 8y³.Solution
2xy = 12 So, xy = (12/2) = 6 ......(i) 3x + 2y = 15 On squaring the above equation, we get, (3x + 2y)² = 15² Or, 9x² + 4y² + 2 × 3x × 2y = 225 Or, 9x² + 4y² + 12 × 6 = 225 (since, xy = 6) Or, 9x² + 4y² = 225 - 72 So, 9x² + 4y² = 153 ....(ii) (3x - 2y)² = 9x² + 4y² - 2 × 3x × 2y = 153 - 12 × 6 = 153 - 72 = 81 {using values from equations (i) and (ii)} Since, 3x > 2y, so, 3x - 2y, cannot be negative. So, 3x - 2y = 9 ....(iii) We know that, a³ - b³ = (a - b) × (a² + b² + ab). So, (3x)³ - (2y)³ = 27x³ - 8y³ = (3x - 2y) × (9x² + 4y² + 3x × 2y) Putting the value of equations (i), (ii) and (iii) in the above equation, we get, = 9 × (153 + 6 × 6) = 9 × (153 + 36) = 9 × 189 = 1,701 Hence, option a.
Section 17(3) mandates that Central Government and specified entities shall:
Consider the following statements regarding confiscation of property acquired through corruption:
Statement 1: Property acquired through corrupt ...
Which kind of hurt is not a grievous hurt?
The decision in the case of R Vs. Bedingfield was overruled in the case of ?
What action is permissible for the Court if it determines that a person accused under section 15 is likely to evade notice service as per the Contempt o...
What does the term “capital account transaction” refer to as per FEMA?
As per Reg 3 of SEBI (Prohibition of Insider Trading) Regulations, 2015, what is the purpose of the provision regarding "legitimate purposes"?
What does the legal maxim Qui Facit Per Alium Facit Per Se imply in the context of the law of agency?
When are the shadow meetings conducted?
Under the Indian Partnership Act, 1932, a partnership at will is one where:
