Question

the sum of two numbers is 437 and their product is 21982. find ttheir difference?

Answer 1

the answer is 58 × 379

= 21982

hope this helps you

btw 58+379=437

Answer 2

Given

we have given sum of two numbers is 437

and Product of numbers is 21982

To Find

we have to find their difference

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let us assume the number be 'x' and 'y'

According to the question:

Sum of two numbers is 437

Then ,our Equation becomes : x+y= 437---(1)

And their product is 21982

Then,our Equation becomes : x y = 21982---(2)

From equation 1

we get ,

=>X= 437 -y ----(3)

Now, substitute X's value from equation 3 into Equation 2

=>x y = 21982

=>(437-y)y=21982

=>437y-y²= 21982

=>21982+y²-437y

=>y²-437y+21982

By using quadratic formula we will solve this Equation

=>y= -b ±√b²-4ac / 2a

a= 1 ,b = -437 & c= 21982

=>y= -(-437) ±√(-437)²-4(1)(21982)/2

=>y= 437±√190969-87928 / 2

=>y = 437±√103041 / 2

Here,the discriminant b²-4ac is >0

So,there will be two real roots

=>y= 437±321 / 2

=>y = 758 /2 or 116/ 2

=>y = 379 or y= 58

From equation 3

x= 437-y

x = 437 -379 or 437-58

=>x= 58 or 379

Hence, we obtain x = 58 or 379

and y = 379 OR 58

finding the difference

x-y = 379-58 & 58-379

$\boxed{\bold{x-y }= \bold{{\red{321\:\&-321}}}}$

We take x-y = $\bold{\red{321}}$( as it gives +ve value )

So , correct value of x = 379 and y = 58

Check:

sum of two numbers is 437

=>x+y = 379+58=437

and their product is 21982= 379× 58=21982