Algebra MCQs

If a + b + c = -11, then what is the value of (a + 4)³ + (b + 5)³ + (c + 2)³ - 3(a + 4)(b + 5)(c + 2)?

If (x + y)³ - (x - y)³ - 3y(2x² - 3y²) = ky³, then find the value of k.

If a³ = 117 + b³ and a = 3 + b, then the value of a + b is?

If $$x + \frac{1}{x} = 3\sqrt 2 ,$$   then what is the value of $${x^5} + \frac{1}{{{x^5}}}?$$

$${\text{If }}\frac{{4\sqrt 3 + 5\sqrt 2 }}{{\sqrt {48} + \sqrt {18} }} = a + b\sqrt 6 {\text{,}}$$       then the value of a and b are respectively?

If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?

If x = √5 + 1 and y = √5 - 1, then what is the value of $$\frac{{{x^2}}}{{{y^2}}} + \frac{{{y^2}}}{{{x^2}}} + 4\left[ {\frac{x}{y} + \frac{y}{x}} \right] + 6?$$

If $$m = \sqrt {5 + \sqrt {5 + \sqrt {5.....} } } $$      and $$n = \sqrt {5 - \sqrt {5 - \sqrt {5.....} } } $$      then among the following the relation between m & n holds is?

If x varies inversely as (y² - 1) and x is equal to 24 when y = 10, then the value of x when y = 5 is?