Question

The sum of a number and its reciprocal is 17/4.find the number

Answer 1

hi there!!!

Solution:

let the number be x and it's reciprocal be 1/x

hence,

x+ 1/x= 17/4

now,

x^2+1 = 17

x 4

now,

multiplying by x,

x^2+1=17/4x

and,

again multiplying by 4,

4x^2+4= 17x

hence,

4x^2-17x+4= 0......required quadratic polynomial.

by factorization method,

4x^2-16x-1x+4=0

4x(x-4) -1(x-4) =0

(x-4) (4x-1) =0

hence,

x=4 or x= 1/4

now,

1.the number=x= 4

hence,

x+1/x=17/4

4+ 1/4= 17/4

16+1/4=17/4

17/4=17/4

Also,

if the number =x=1/4

then,

1/4+4/1=17/4

1/4+4=17/4.....(as 4/1=4)

16+1/4=17/4

17/4=17/4

hence,

the number= 4 and 1/4

hope this helps!! ☺✌♥

Answer 2

Answer:

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