Question

x and x+1 are the two continuous natural numbers, then (i) Write the next two natural numbers. (ii) Find the product of first and the fourth number. (iii) Find the product of second and the third number. (iv) Find the relation between these products.

Answer 1

Explanation:

x is followed by x+1 so each time we add one

our sequence goes like this:

• x
• x+1
• x+1+1⇒ x+2
• x+2+1⇒x+3

the first number is x and the fourth one is x+3

• x*(x+3)
• x²+3x

the second number is x+1 and the third one is x+2

• (x+1)(x+2)
• x²+2x+x+2
• x²+3x+2

the first product is x²+3x and the second one is x²+3x+2

Let P be x²+3x and P' be x²+3x+2

• P'-P = 2
• P' = P+2

Answer 2

(i) X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) x( x+4)=a

(x+1)(x+3)= a+3

Explanation:

(i) X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;

x(x+4)=a

(x+1)(x+3)= a+3