Mohan, Aman and Sohan together can complete a work in 18 days. If Mohan can work thrice as faster than Aman and Aman can work twice as faster than Sohan, then in how many days Sohan alone can complete the same work?

If a = 5 + √6, b = 5 - √6, then what is the value of a² + b²?

If a = 7 + √2, b = 7 - √2, then what is the value of a² + b²?

If $$2x - \frac{1}{2x} = \frac{10}{3}$$​ and x > 1, then find the value of $$x^2+\frac1{16x^2 }$$​​

If x² - y² = 255 and x + y = 17, then find x - y.

The cost of a table exceeds that of a chair by ₹5,000. If the combined price of 16 tables and 14 chairs amounts to ₹2,00,000, determine by what percentage the price of a chair is less than the price of a table.

The difference of squares of two consecutive odd numbers is 56. What is the sum of the two numbers?

If a = 3 + √2, b = 3-√2, then what is the value of a² + b²?

Solve the following system of 3 equations in 3 unknowns.
x - 3z = -5
2x - y + 2z = 16
7x - 3y - 5z = 19

If x+y+z=0, where none of x,y and z is equal to 0 , then find the value of $$\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$$​​