Question

If the sum of the number and its reciprocal is equal to 10\3 find the cube of the number

Answer 1

Answer:

3

Step-by-step explanation:

Let the number be x. Given sum of number and it's reciprocal is 103.

∴x+1x=103

∴3x2−10x+3=0

∴3x2−9x−x+3=0

∴(3x−1)(x−3)=0

∴x=3 or x=13

Thus the number is 3.

Short cut:

The sum is 103. So it's safe to say x would be a multiple of 3. Try all the possible values.

Here 3+13=103

Thus 3 is the required number.