The sum of the squares of two consecutive natural numbers is 25. Represent this situation in the form of a quadratic equation.
The sum of the squares of two consecutive natural numbers is 25. Represent this situation in the form of a quadratic equation.
A) x2 + (x + 1)2 + 25 = 0
B) x2 – (x + 1)2 = 25
C) x2 + (x + 1)2 = 25
D) (x + 1)2 – x2 = 25
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Correct option is (C) x2 + (x + 1)2 = 25
Since, difference between two consecutive natural numbers is 1.
Let x & (x+1) be two consecutive natural numbers.
\(\therefore\) Sum of squares of consecutive natural numbers is \(x^2+(x+1)^2.\)
Given that the sum of the squares of two consecutive natural numbers is 25.
\(\therefore\) \(x^2+(x+1)^2=25\) which represent the given situation.
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