Question 181778This question is from textbook Algebra
: the sum of the reciprocals of two consecutive even integers is 11/60. what are the integers? This question is from textbook Algebra
You can put this solution on YOUR website! 1/x+1/(x+2)=11/60
(x+2+x)/x(x+2)=11/60
(2x+2)/(x^2+2x)=11/60
2x+2=11(x^2+2x)/60
2x+2=(11x^2+22x)/60
120x+120=11x^2+22x
11x^2+22x-120x-120=0
11x^2-98x-120=0
Using the quadratic equation x = (-b +- sqrt( b^2-4*a*c ))/(2*a) we get:
x=(98+-sqrt[-98^2-4*11*-120])/2*11
x=(98+-sqrt[9604+5280])/22
x=(98+-sqrt14884)/22
x=(98+-122)/22
x=(98+122)/22
x=220/22
x=10 ans.
proof:
1/10+1/12=11/60
(12+10)/120=11/60
22/120=11/60
11/60=11/60
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