Q7 of 168 Page 7

Find three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154.

Let the first number be ‘X’, so the other numbers will be ’(X+1)’ & ‘(X+2).


∵ X2 + (X + 1)(X + 2) = 154


X2 + X2 + 2X + X + 2 = 154


On simplifying further,


2X2 + 3X – 152 = 0


On applying Sreedhracharya formula







X = – 9.5 or 8


∴ X = 8 (Only whole values)


∴ X +1 = 9


∴ X + 2 = 10


∴ The numbers are 8, 9 & 10.


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