Question

Prove that if x and y are odd positive integers ;x>y. Then x^2-y^2 is divisible by 4​

Answer 1

Answer:

Since x and y are odd positive integers so

Let x = 2n + 1 and y = 2m + 1

x² + y² = (2n + 1)² + (2m + 1)²

= 4(n² + m²) + 4(n + m) + 2

= 4 {(n² + m² + n + m}) + 2

= 4q + 2

Where q = n² + m² + n + m is an integer

Since

x² + y² is even and leaves remainder 2 when divided by 4

x² + y² is even and leaves remainder 2 when divided by 4 Not divisible by 4

Answer 2

Six bananas to be crushed into a pulp. Half a litre of milk to be boiled. Banana pulp and sugar to be added to the mixture. It should be stirred for two minutes and then removed from the heatRead the given statements and select the correct option.

(i) Obesity and excessive fat intake increases the likelihood of being an overweight adult; this

can put the individual at risk for cardiovascular diseases and other health problems.

(ii) A diet, heavily dependent on fast food, results in decreased energy, excess fat and a

deficiency of calcium, riboflavin, vitamin A , folic acid and fibre.

a) Both (i) and (ii) are true

b) (i) is true and (ii) is false

c) (i) is false and (ii) is true

d) Both (i) and (ii) are falseRead the given statements and select the correct option.

(i) Obesity and excessive fat intake increases the likelihood of being an overweight adult; this

can put the individual at risk for cardiovascular diseases and other health problems.

(ii) A diet, heavily dependent on fast food, results in decreased energy, excess fat and a

deficiency of calcium, riboflavin, vitamin A , folic acid and fibre.

a) Both (i) and (ii) are true

b) (i) is true and (ii) is false

c) (i) is false and (ii) is true

d) Both (i) and (ii) are falseThey have 'found' a ball yesterday Write the parts of speech of the inverted word.They have 'found' a ball yesterday Write the parts of speech of the inverted word.