Question

If (x + y) = 10 and xy =
16 find the value (x- y)^2

Answer 1

Given:

• Given:x + y = 10

• Given:x + y = 10x.y = 16

Given:x + y = 10x.y = 16Working

Given:x + y = 10x.y = 16WorkingIf x.y = 16

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/x

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10

1. Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by x

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xTherefore

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation gives

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0Either (x-8) = 0

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0Either (x-8) = 0Or (x-2) = 0

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0Either (x-8) = 0Or (x-2) = 0(because one of those factors has to be zero to give a product of zero on RHS of equation)

Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0Either (x-8) = 0Or (x-2) = 0(because one of those factors has to be zero to give a product of zero on RHS of equation)Solution is

• Given:x + y = 10x.y = 16WorkingIf x.y = 16Then y = 16/xSubstitute for y in x + y = 10Therefore x + 16/x = 10Multiply throughout by xThereforex2 + 16 = 10x (note by writing x2 I mean x-squared)Subtracting 10x from each side of the equation givesx 2 - 10x + 16 = 0Solving the quadric equation gives factors(x - 8) (x-2) = 0Either (x-8) = 0Or (x-2) = 0(because one of those factors has to be zero to give a product of zero on RHS of equation)Solution isx = 8 or x = 2