Question

If the sum of two numbers is 48 and their gcd and lcm are 2 and 286 then what is the sum of the inverse of those numbers?​

Answer 1

Step-by-step explanation:

let the ratio of the no. be x : y

then the no. be (gcd ×ratio)

no. be 2x and 2y

sum of the no. = 48

2x+2y= 48

x+y= 48/2=24

LCM of the no. = 286

2×x×y= 286

xy= 143

(x-y)²= (x+y)²-4xy

(x-y)² = (24)²-4×143

(x-y)²= 576- 572

(x-y)²= 4

x-y= 2

x+y= 24

on adding both eq

2x= 26

on subtracting both eq.

2y= 22

the no is 2x and 2y

hence no. be 26 and 22

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