List of top Mathematics Questions on Simplification

If \( \sqrt{3}x - 2 = 2\sqrt{3} + 4 \), then the value of \( x \) is:

If \(\frac{x}{(b + c)(b + c - 2a)} = \frac{y}{(c - a)(c + a - 2b)} = \frac{z}{(a - b)(a + b - 2c)}\), then the value of \(x + y + z\) is:

Given expression:
\(\frac{(0.682)^2-(0.318)^2}{0.682-0.318}\)

Among P, Q, R, S, T, each having different weight. R is heavier than only P and S is lighter than Q and heavier than T. Who among them is the heaviest?

The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$