The difference between two numbers is 43 and their product is 50 what is the sum of the numbers

Solution

Let the two numbers are $$a$$ and $$b$$

Given, Product of numbers = 50

$$=$$> $$ab = 50$$

Difference of numbers = 43

$$=$$> $$a - b = 43$$

$$=$$> $$\left(a-b\right)^2=43^2$$

$$=$$> $$a^2+b^2-2ab=1849$$

$$=$$> $$a^2+b^2-2\left(50\right)=1849$$

$$=$$> $$a^2+b^2=1849+100$$

$$=$$> $$a^2+b^2=1949$$

$$ \therefore\ $$Sum of the squares of the numbers = 1949

Hence, the correct answer is Option B

The Sum of Two Numbers is 43 and Their Difference is 50

The sum of two numbers is 43 and their difference is 50. What are the two numbers? Let's start by calling the two numbers we are looking for x and y. The sum of x and y is 43. In other words, x plus y equals 43 and can be written as equation A:

x + y = 43

The difference between x and y is 50. In other words, x minus y equals 50 and can be written as equation B:

x - y = 50

Now solve equation B for x to get the revised equation B:

x - y = 50
x = 50 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 43
50 + y + y = 43 50 + 2y = 43 2y = -7

y = -3.5

Now we know y is -3.5. Which means that we can substitute y for -3.5 in equation A and solve for x:

x + y = 43
x + -3.5 = 43
X = 46.5

Summary: The sum of two numbers is 43 and their difference is 50. What are the two numbers? Answer: 46.5 and -3.5 as proven here:

Sum: 46.5 + -3.5 = 43
Difference: 46.5 - -3.5 = 50

Sum Difference Calculator Do you want the answer to a similar problem? Enter the sum and difference here to find the two numbers:

The Sum of Two Numbers is 43 and Their Difference is 51

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