Question

Check my work please!

The sum of the reciprocals of two consecutive integers is -9/20. find the integers.

So
1x+1x+1=−920

1×(x+1)x×(x+1)+1×x(x+1)×x=−920

(x+1)+(x)x2+x=−920

2x+1x2+x=−920

Cross multiply them,
20(2x+1)=−9(x2+x)

40x+20=−9x2−9x

Equate them to 0 to form a quadratic equation,
9x2+49x+20=0


Solving for quadratic equation would give you
x = -5 or x = -0.444.

SInce x is an integer, x = -5.

The two integers are -5 and -4.

Answer 1

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