We have, Let the two odd consecutive numbers So, According to given question, If, If, So, Hence, this is the answer. > Solution Let the two consecutive odd numbers be x and x+2. ATQ, X2 + (X+2)2 = 394 X2 + X2 + 4X + 22 = 394 2X2 + 4X + 4 = 394 .......( dividing the equation by 2) X2 +2X =(394 - 4)/2 X2 + 2X = 195 X2 +2X - 195 = 0 X2 + 15X - 13X -195 = 0 .............( by factorization meathod ) X( X + 15 ) - 13( X + 15 ) = 0 ( X + 15 ) ( X - 13 ) X = -15 OR X = 13 CASE 1 If X = -15, then, X + 2 = - 13 CASE 2 If X = 13, then, X + 2 = 15 Suggest Corrections 16 Find two consecutive odd natural numbers, the sum of whose squares is $$202$$. We have, Let the two odd consecutive numbers $$x\,\text{and}\,x+2$$ So, According to given question, $$ {{x}^{2}}+{{\left( x+2 \right)}^{2}}=202 $$ $$ \Rightarrow {{x}^{2}}+{{x}^{2}}+4+4x=202 $$ $$ \Rightarrow 2{{x}^{2}}+4x=198 $$ $$ \Rightarrow {{x}^{2}}+2x=99 $$ $$ \Rightarrow {{x}^{2}}+2x-99=0 $$ $$ \Rightarrow {{x}^{2}}+\left( 11-9 \right)x-99=0 $$ $$ \Rightarrow {{x}^{2}}+11x-9x-99=0 $$ $$ \Rightarrow x\left( x+11 \right)-9\left( x+11 \right)=0 $$ $$ \Rightarrow \left( x+11 \right)x-9=0 $$ If, $$ x+11=0 $$ $$ \Rightarrow x=-11 $$ If, $$ x-9=0 $$ $$ x=9 $$ So, $$x+2=9+2=11$$ Hence, this is the answer. Chrissy C. this is a question about factoring word problems 2 Answers By Expert Tutors |