If (a+b+c) = 14, and (a³ + b³ + c³ - 3abc) = 98, find the value of (a² + b² + c²).

Which one of the following pairs is not correctly matched?

If x + y = 2z, then the value of $$\frac{x}{x - z} + \frac{z}{y - z}$$​ is

If O be the centre of the incircle of a triangle ABC and ∠BOC = 110°, then the value of ∠BAC will be- 

If $$x^4 + \frac{1}{x^4} = 14$$​, then the value of $$x^3 + \frac{1}{x^3}$$​ is
A. $$3\sqrt{6}$$​​
B. $$\frac{18}{\sqrt{6}}$$​​

C. $$9\sqrt{\frac{2}{3}}$$​​
D. $$3\sqrt{2}$$​​

The sum of the squares of two numbers is 545 and the square of their difference is 1. Find the product of the two numbers.

If $$x + y = 5$$ and xy = 4 , find the value of $$x^3 + y^3$$​.

The value of $$\left(x^{\frac{2}{3}} - x^{\frac{1}{3}}y^{\frac{1}{3}} + y^{\frac{2}{3}}\right)\left(x^{\frac{1}{3}} + y^{\frac{1}{3}}\right)$$​ is

(x + y + 2z)(x + y) can be expressed as

If $$x + \frac{1}{x} = 3$$, then $$x^2 + \frac{1}{x^2}$$ is:

If ​​​​​ $$a²- 4a +1= 0$$, find $$a² + \frac{1}{a^2}$$.​