Practice Algebraic Identities Practice Questions with Detailed Solutions – Level 3

If \(x + \dfrac{1}{x} = \sqrt{5},\) what is the value of \(x^{5} + \dfrac{1}{x^{5}}?\)

If \(a + b + c = 0,\) where \(a,\) \(b\) and \(c\) are not all zero, what is the value of \((a^{2} + b^{2} + c^{2})^{2}\) \({}\div (a^{4} + b^{4} + c^{4})?\)

If \(a + b + c = 6,\) \(a^{2} + b^{2} + c^{2} = 14\) and \(abc = 6,\) what is the value of \(a^{3} + b^{3} + c^{3}?\)

Simplify: \( \frac{(2.3)^3 - 0.027}{(2.3)^2 + 0.69 + 0.09} \)

If \(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 0\) and \(a + b + c = 9,\) where \(a,\) \(b\) and \(c\) are non-zero real numbers, what is the value of \(a^{2} + b^{2} + c^{2}?\)

If \(x - y = 4\) and \(xy = 21,\) what is the value of \(x^{3} - y^{3}?\)

If \(a + b = 10\) and \(a^{2} + b^{2} = 58,\) what is the value of \(a^{4} + b^{4}?\)

If \(x = 3 + 2\sqrt{2},\) what is the value of \(x^{3} + \dfrac{1}{x^{3}}?\)

If \(x = 97,\) \(y = 98\) and \(z = 99,\) what is the value of \(x^{3} + y^{3} + z^{3} - 3xyz?\)

What is the value of the following product?

\(\left(1 - \frac{1}{2^{2}}\right)\left(1 - \frac{1}{3^{2}}\right)\left(1 - \frac{1}{4^{2}}\right)\) … \(\left(1 - \frac{1}{20^{2}}\right)\)