Algebra MCQs

If a + b + c = 0, then the value of $$\frac{1}{{\left( {a + b} \right)\left( {b + c} \right)}} + $$   $$\frac{1}{{\left( {a + c} \right)\left( {b + a} \right)}} + $$   $$\frac{1}{{\left( {c + a} \right)\left( {c + b} \right)}}$$   $$ = ?$$

The lines 2x + y = 5 and x + 2y = 4 intersect at the point?

If $$\sqrt x + \frac{1}{{\sqrt x }} = 3,$$   then the value of $${x^3} + \frac{1}{{{x^3}}}$$  is:

If a + b + c = 26 and ab + bc + ca = 109, find the value of a² + b² + c² = ?

If $$\frac{{b - c}}{a}$$  + $$\frac{{a + c}}{b}$$  + $$\frac{{a - b}}{c}$$  = 1 and a - b + c ≠ 0 then which one of the following relations is true ?

If a + b = 1 and a³ + b³ + 3ab = k, then the value of k is?

What is the simplified value of $$\left( {x + \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^4} + \frac{1}{{{x^4}}}} \right)\left( {{x^8} + \frac{1}{{{x^8}}}} \right)\left( {{x^{16}} + \frac{1}{{{x^{16}}}}} \right){\text{is:}}$$

If ax² + bx + c = a(x - p)², then the relation among a, b, c would be?

The value of $$\frac{1}{4} + \frac{{\left[ {{{\left( {20.35} \right)}^2} - {{\left( {8.35} \right)}^2}} \right] \times 0.0175}}{{{{\left( {1.05} \right)}^2} + \left( {1.05} \right)\left( {27.65} \right)}}{\text{is:}}$$