Question 188
The sum of the squares of two consecutive positive numbers is 1861. What are the two numbers ?
Solution
Let two consecutive numbers be $$(x)$$ and $$(x+1)$$
Acc to ques :
=> $$(x)^2 + (x+1)^2 = 1861$$
=> $$2x^2 + 2x + 1 - 1861 = 0$$
=> $$x^2 + x - 930 = 0$$
=> $$x^2 + 31x - 30x - 930 = 0$$
=> $$x(x+31) - 30(x+31) = 0$$
=> $$(x+31) (x-30) = 0$$
=> $$x = 30 , -31$$
Since, numbers are positive, => $$x = -31$$ is not possible.
=> Numbers are = 30 & 31
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