Suppose (x+y)² = 18 and (x-y)² = 12. Find the value of x² + y².

It is given 3^x = \(\dfrac{2}{9}\) and 3^y = 27. Find the value of 3^3x+2y.

Find the value of a in 10x³ + ax² + 5x + 2 by expanding (2x² + 1)(5x + 2)

Solve for the value of m in each of the following:

(a) 5^m . 25^2m = 125^2m-1

(b) 5^m . 25^m . 125^m . 625^m = 5³⁰ 

If a = 5x² - 4x + 2 and b = 5x² - 4x - 3, is a > b true?

If 2^a x 3^b = 2^c x 3^d = 36, find the value of (a-1)(d+1)+(b+1)(c-1).

If (x+y)² = 9 and (x-y)² = 1, x² + y² = ?

what is the value of n in 3²ⁿ⁺¹+4ⁿ=259?

What is the ones digit of 7²⁵?