Get 2 FREE Instant-Explanations on Filo with code FILOAPP

The sum of squares of two consecutive natural numbers is 244;

Question

The sum of squares of two consecutive natural numbers is 244; find the numbers.

Views: 546 students

Found 2 tutors discussing this question

Evelyn Discussed

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Let the two consecutive natural numbers be

x

and

x + 2

Sum of squares of these two consecutive natural numbers is 244

x^{2} + (x + 2)^{2} = 244

\Rightarrow x^{2} + x - 6 = 84

\Rightarrow x^{2} + x^{2} + 4 + 4 x = 244

\Rightarrow 2 x^{2} + 4 x - 240 = 0

\Rightarrow x^{2} + x - 120 = 0

\Rightarrow x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

\Rightarrow x = \frac{- 2 \pm 2 ^{2} - 4 \times 1 \times ( - 120 )}{2}

\Rightarrow x = \frac{- 2 \pm 4 + 480}{2}

\Rightarrow x = \frac{- 2 \pm 484}{2}

\Rightarrow x = \frac{- 2 \pm 22}{2}

\Rightarrow x = \frac{- 2 + 22}{2}, \frac{- 2 - 22}{2}

\Rightarrow x = \frac{20}{2}, \frac{- 24}{2}

\Rightarrow x = 10, - 12

But age cannot be negative so,

The two numbers are

10

and

10 + 2 = 12.

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	The sum of squares of two consecutive natural numbers is 244; find the numbers.
Answer Type	Text solution:1
Upvotes	150