Question

Show that (x-1)(x-2)(x-3)(x-4) +1 is a perfect square

Answer 1

(x-1)(x-2)(x-3)(x-4)+1

(x-1)(x-2)(x-3)(x-4)=1

(x-1)(x-2)(x-3)=(x-4)

x(x-2)-1(x-2)=x(x-3)-4(x-3)

x(x-2)-1(x-2)=x(x-3)-4(x-3)

x2-2x-1x+2=x2-3x-4x+12

-3x+7x=12-2

4x=10

X=2.5

Putting the value of x

(2.5+1)(2.5+2)(2.5+3)(2.5+4)+1

3.5*4.5*5.5*6.5+1

63.5625

x(x-2)-1(x-2)=x(x-3)-4(x-3)

x2-2x-1x+2=x2-3x-4x+12

-3x+7x=12-2

4x=10

X=2.5

Putting the value of x

(2.5+1)(2.5+2)(2.5+3)(2.5+4)+1

3.5*4.5*5.5*6.5+1

63.5625

this is a prfect square