Question

Of the difference between a number and it's reciprocal is 24/5 find the number​

Answer 1

Answer:

Explanation:

let the number be 'a'

then, according to the question,

a-1/a=24/5

a^2-1=(24/5)a

5(a^2-1)=24a

5a^2+24a-5=0

5a^2+25a-a-5=0.

5a(a+5)-1(a+5)=0.

(5a-1)(a+5)=0.

5a-1=0,a=1/5

or, a+5=0,a=-5.

but only a=1/5 satisfies the condition, so

answer is a=1/5.

Answer 2

Answer:

let the number is x and its reciprocal is 1/x

given that

x-1/x = 24/5

(x²-1) /x = 24/5

5x²-5 = 24x

5x²-24x-5= 0

5x²-25x+x-5=0

5x(x-5)+1(x-5)= 0

(x-5)(5x+1) = 0

x= 5,-1/5