If 5x + 4y = 12 and xy = 2, then find the value of 125x³ + 64y³.

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 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?

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

If a + b = 13 and $$a^3+b^3=559$$​. Find the value of $$a^2+b^2 .$$​​

If two natural numbers a and b are such that $$a^2-b^2=17,a>b$$​ ，then a possible value of $$a^2+b^2-ab$$​ will be

If x + $$\frac 1x$$​= –1, then compute: $$x^4 + \frac{1}{x^4} + 2x^2 + \frac{2}{x^2}$$​​