Question

Find two consecutive positive integers,sum of whose square is 183.

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Answer 1

Let the first number be x,

there second number will be (x+1)

According to question,

x² + (x + 1)² = 183 (using (a+b)² = a² + b² + 2ab)

x² + x² + 1² + 2(x)(1) = 183

2x² + 2x + 1 = 183

2x² + 2x = 183 - 1

2(x² + x) = 182

x² + x = 182/2

x² + x = 91

x² + x - 91 = 0

As the the quadratic equation we got does not have integral roots. Therefore, we can conclude that:

No two consecutive positive integers whose sum is 183 exist.

Answer 2

Answer:

Hence, the two consecutive positive integers are 13 and 14.

Step-by-step explanation:

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Class 10

>>Maths

>>Quadratic Equations

>>Solutions of Quadratic Equations

>>Two consecutive positive integers, sum o

Question

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Two consecutive positive integers, sum of whose squares is 365 are

Medium

Solution

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Correct option is A)

Let the two consecutive positive integers be x and x+1

Then,

x

2

+(x+1)

2

=365

⇒x

2

+x

2

+2x+1=365

⇒2x

2

+2x−364=0

⇒x

2

+x−182=0

Using the quadratic formula, we get

x=

2

−1±

1+728

⇒

2

−1±27

⇒x=13 and x=−14

But x is given to be a positive integer. ∴x



=−14

Hence, the two consecutive positive integers are 13 and 14.

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