Average of 8 numbers is 47. The average of first three numbers is 53 and the average of next two numbers is 55. If the sixth number is 7 and 10 less than seventh and eighth number respectively, then what is the value of eighth number?

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

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

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 $$\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$$​​