Question

the sum of number and its reciprocal is 10 by 3 find the number

Answer 1

Let the number be x

X + 1/X = 10/3

Multiply the equation by 3X (type of lcm)

3X^2 + 3 = 10X

3X^2 - 10X + 3 = 0

3X^2 - 9X - X + 3 = 0

3X (X - 3) - 1 (X - 3) = 0

(3X - 1) (X- 3) = 0

So,

The number can be 3 or 1/3

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Answer 2

let the number be x , and the reciprocal of this number is 1/x,
by condition,
x+1/x =10/3
(x^2+1)/x =10/3
x^2+1 = 10x/3
3(x^2+1)=10x
3x^2+3=10x
3x^2-10x+3=0
3x^2-9x-x+3=0
3x(x-3)-1(x-3)=0
(3x-1)(x-3)=0
3x-1=0 and x-3 =0
x=1/3. and x= 3

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