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The sum of the squares of two consecutive odd number is 394 find the number

Posted by Komal Sharma 8 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Hans Raj 8 years, 6 months ago

let the numbers be x and x+2

x2 + (x+2)2 = 394

x2+x2+4+4x=394

2x2+4x+4=394

x2+2x+2=197

x2+2x-195=0

x2+15x-13x-195=0

x(x+15) - 13(x+15)=0

(x+15)(x-13)=0

x+15=0 or x-13=0

x= -15 or x=13

but x= -15 is not possible as it is - ve number

therefore one odd number is x = 13

next consrcutive odd number is x+2 = 13+2=15

13 and 15 are two consecutive positive odd numbers

check your answer 13²+ 15²= 13x13 + 15x15 = 169+225=394

1Thank You

Rohit Sharma 8 years, 6 months ago

First consecutive no.x and second con.no.=x+1 x²+(x+2)²=394 x²+x²+4x+4=394 2x²+4x-390=0 x²+2x-195=0 x²+15x-13x-195=0 x(x+15)-13(x+15)=0 (x+15)(x-13)=0 x+15=0 , x-13=0 x=-15 , x=13 Ist cons.no.=13 IInd cons.no.=13+2=15

2Thank You

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