Question

three consecutive positive integers such that square of first integer when added to the product of the other two integers the sum is 154 find the integers

Answer 1

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Answer 2

Let the three consecutive positive integers be x,x+1, x+2.

Given that square of the first integer when added to the product of other two integers the sum is 154.

x^2 + (x + 1)(x + 2) = 154

x^2 +  x^2 + 2x + x + 2 = 154

x^2 + x^2 + 3x + 2 = 154

x^2 + x^2 + 3x = 152

2x^2 + 3x - 152 = 0

2x^2 - 16x + 19x - 162 = 0

2x(x - 8) + 19(x - 8) = 0

(2x + 19)(x - 8) = 0

2x = -19 and x = 8

x = -19/2.

Since x cannot be negative,so x = 8.

Then,

x = 8

x + 1 = 9

x + 2 = 10.


Therefore the integers are 8,9,10.


Verification:

8^2 + (9 * 10) = 154

64 + 90 = 154

154 = 154.


Hope this helps!