divisibility

 Let x and y be integers. Prove that (2x + 3y) is divisible by 17 if (9x + 5y) is divisible by 17.

Simultaneous equation

If  S = x² + y²

And T = xy

Express x and y in terms of S and T

logarithm

Solve:

miscellaneous equations

Solve for x and y

x² - xy + y² = 39

x³+ y³ = 351

miscellaneous equations

Solve for x and y:

x² + xy + y² = 37

x³- y³ = 37

miscellaneous equations,

Solve:   

 x⁴ + x²y² + y⁴ = 21

 x² + xy + y² = 7

miscellaneous equations

Solve the equation: x - y = 1

x³- y³ = 19

miscellaneous equations

Solve the equations:

X³+ y³ = 35

X + y = 5

miscellaneous equations

Solve the equation:

X² – 25y² = 156

X + 5y = 26

making the subject of the equation

The two expressions

                                      and                                          
 
are found by different methods for volume of a certain solid. Prove that they are equivalent provided that 

                       London Matriculate

algebra

logarithm

 

logarithm

 

algebra

 

Rationalization

Algebra

if 2/x = 1/a + 1/b then find 1/(x -a)  + 1/ (x -b)

Algebra

show that:
If (a + 1/a)^2 = 3. 

a^3 + 1/ a^3 = 0

Algebra

Prove that {a /(a-b)} + {b/(b-c)} + {c/(c -a)} = 3 - [{a /(a-c)} + {b/(b-a)} + {c/(c -b)}]

factorize

factorize: (a + b)(a - b) - 4c(a -c)

Arithmetic Progression

In an AP if the 8th term is twice the 13th, show that the 2nd term is twice the 10th term