Three consecutive natural no.are such that ...

Three consecutive natural no.are such that the squares of the middle no. Exceeds the difference of the square of the other two by 60.find the no.

 

Plz Plz ans.this

  • 1 answers

Rashmi Bajpayee 2 years, 12 months ago

Let the three consecutive natural numbers be x, x + 1 and x + 2.

Then, According to question,

{tex}{\left( {x + 1} \right)^2} = {\left( {x + 2} \right)^2} - {x^2} + 60{/tex}

=>          {tex}{x^2} + 2x + 1 = {x^2} + 4x + 4 - {x^2} + 60{/tex}

=>          {tex}{x^2} - 2x - 63 = 0{/tex}

=>          {tex}{x^2} - 9x + 7x - 63 = 0{/tex}

=>          {tex}x(x-9)+7(x-9)=0{/tex}

=>          {tex}(x-9)(x+7)=0{/tex}

=>          {tex}x=9{/tex} and {tex}x=-7{/tex} (neglected, as it is not a natural number)

Therefore, the three consecutive natural numbers are 9, 10 and 11.

Related Questions:

Completing square
  • 1 answers
Ap questions not in ncert text
  • 2 answers
How to solve equations
  • 0 answers

Buy Complete Study Pack

Subscribe complete study pack and get unlimited access to selected subjects. Effective cost is only ₹ 12.5/- per subject per month. Based on the latest CBSE & NCERT syllabus.

myCBSEguide App

myCBSEguide

Trusted by 70 Lakh Students

CBSE Test Generator

Create papers in minutes

Print with your name & Logo

Download as PDF

3 Lakhs+ Questions

Solutions Included

Based on CBSE Blueprint

Best fit for Schools & Tutors

Work from Home

  • Work from home with us
  • Create questions or review them from home

No software required, no contract to sign. Simply apply as teacher, take eligibility test and start working with us. Required desktop or laptop with internet connection