Madhya Pradesh Police Exam Model Paper 4

Question : 81 of 100

Marks: +1, -0

Find two consecutive odd positive integers, sum of whose square is 290?

Solution:

Let the numbers be x and

(x + 2)

respectively

⇒x^2+(x+2)^2=290

⇒x^2+x^2+4+(2×x×2)=290

⇒2x^2+4+4x=290

⇒2x^2+4x=290-4

⇒2x^2+4x=286

⇒x^2+2x-143=0

⇒x^2+2x-143=0

⇒x^2+13x-11x-143=0

⇒x(x+13)-11(x+13)=0

⇒(x-11)(x-13)=0

⇒x=11,-13

The number can't be negative so value of x is 11
Second number

= 11 + 2 = 13

∴ The consecutive odd integers are 11 and 13

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