Question

solve the following equation in two variable

Answer 1

Let the four consecutive natural numbers be x,x+1,x+2,x+3.

Given that product of four consecutive natural numbers is 840.

= > x * (x + 1) * (x + 2) * (x + 3) = 840

= > x^4 + 6x^3 + 11x^2 + 6x - 840 = 0

= > x^4 + 10x^3 + 51x^2 + 210x - 4x^3 - 40x^2 - 204x - 840 = 0

= > x(x^3 + 10x^2 + 51x + 210) - 4(x^3 + 10x^2 + 51x + 210) = 0

= > (x - 4)(x^3 + 10x^2 + 51x + 210) = 0

= > (x - 4) = 0, (x^3 + 10x^2 + 51x + 210) = 0[Neglect it as it is real and imaginary)

= > x - 4 = 0

= > x = 4.

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1st number:

= > x + 1 = 5

= > x + 2 = 6

= > x + 3 = 7.

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Therefore, the numbers are 4,5,6,7.

Hope this helps!