Two rectangular fields have lengths \(x\) and \(y\) meters respectively, where \(x > y\). The sum of their lengths is equal to three times the difference of their lengths. What is the value of \(\dfrac{3xy}{2(x^{2} - y^{2})}\)?

Simplify: (a + b)² − (a − b)²

If x = 3, what is the value of the expression x² + 2x + 1?

Simplify: (3a + 2b)² + (3a − 2b)² − 2(9a² + 4b²)

To a square plot having an area of \(x\;\mathrm{m}^{2}\), a strip having an area of \(\dfrac{1}{4}\sqrt{x}\;\mathrm{m}^{2}\) and a patch having an area of \(a^{2}\;\mathrm{m}^{2}\) are added. If the total area can now be expressed as a perfect square using powers of \(x\) and constants, find the positive value of \(a\).

Simplify: \(\left(\frac{17a^{5}b^{2}c^{4}}{51a^{3}b^{3}c^{4}}\right)\times 9b^{3}\)

If \(a+b+c=6\), \(abc=-60\) and \(a^3+b^3+c^3=162\), find the value of \(ab+bc+ca\).

Which of the following equations represent the statement, \"one fifth of m is twice of one third of n\"?

Find the value of \(x + \frac{1}{x}\) if \(\sqrt{x} + \frac{1}{\sqrt{x}} = 3\).

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 26x + 165 = 0

II. y² – 38y + 357 = 0

Factorize the following:

(x ²- 6xy + 9y ²) - 25

If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that

AP = PQ = QB, then the mid point of PQ is 

If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?