Question

if the sum of two number is 42 and their product is 437, then find the absolute difference between the numbers?with soluction full

Answer 1

Answer:

Step-by-step explanation:

x+y = 42 (Given)

xy = 437 (Given)

Thus, solving for one variable in terms of the other -

x = 42-y

= (42-y)y = 437

=  -y²+42y = 437

= y²-42y = -437

= y²-42y+437 = 0

Using the formula of quadratic equation   y = -b ±√(b²-4ac)/ 2a

= y = 42 ±√((-42)²-4(1)(437))/2

= y = 21 ±(√(1764 - 1748))/2

= y = 21 ±(√16)/2

= y = 21 ± 4/2

 = y = 21 ± 2

 = y = 21 or 23

If y = 21 then x+21 = 42 and x = 21

If y = 23  then x+23 = 42,  x=19

x= 19, y = 23

Difference:  23-19 = 4      

Answer 2

Answer:

Absolute difference between the numbers = |x-y|=4

Step-by-step explanation:

Let x , y are two numbers,

sum of two numbers = 42

=> x+y = 42 ---(1)

Product of two numbers =437

=> xy = 437 ---(2)

/* We know the algebraic identity:

(a-b)² = (a+b)²-4ab */

$Now, //(x-y)^{2}=(x+y)^{2}-4xy$

$=(42)^{2}-4\times 437$

$=1764 - 1748$

$=16$

$x-y = ±\sqrt{16}\\=±4$

Therefore,

Absolute difference between the numbers = |x-y|=4

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